The substitute struck twice as Chelsea scored three times in eight minutes for a 3-2 comeback victory at Southampton.
The France striker then channelled that never-say-die spirit again when insisting the Blues cannot admit defeat in their top-four quest, despite still trailing fourth-placed Tottenham by seven points.
“As long as mathematically it is going to be possible, we are going to believe,” said Giroud.
“So we take the games one by one and we have maybe five or six finals to play. Let’s do the job and we will see what the other teams do.”
Relegation-threatened Southampton stunned Chelsea by sweeping into a two-goal lead thanks to strikes from Dusan Tadic and Jan Bednarek.
The Blues turned the game on its head thanks to Giroud’s smart brace, however, and another neat finish from Eden Hazard.
Giroud hailed his first two league goals for Chelsea and then paid tribute to the character of Antonio Conte’s men.
A sensational turnaround by the Blues! 🔥⁰
— Chelsea FC (@ChelseaFC) April 14, 2018
“Obviously I was waiting for that,” Giroud told Chelsea’s official website of his first Premier League goals for the Blues.
“I have tried so many times to put it in the back of the net. When you are a striker you need to keep going and keep your confidence high, even if I have been playing a bit less in these recent weeks.
“I always used to say that football is an ever-lasting beginning, so you always need to question yourself and in those moments the most important thing is to show some character.
“I have been through some difficult periods in my career and all the time I try to come back stronger and it has happened again in this game, and I am very pleased for me and for the team.”
Victory would have given Southampton’s survival hopes a major boost. Instead defeat left Mark Hughes’ men five points adrift of safety.
New Saints boss Hughes insists his players can cope with the pressure, despite their increasingly precarious position.
“They’ve taken blows all year, they can’t start feeling sorry for themselves now, it’s gone beyond that,” said Hughes.
“We’ve got to stick our chests out, get on with it, start being men and take responsibility.
“I thought they did that today, and against Arsenal. I think we’ve still got enough to get out of this.”
Jose Mourinho has ordered Manchester United’s record-signing Paul Pogba to show consistency on the training ground, as well as in competitive action, following his stunning display against Premier League leaders Manchester City last weekend.
The France international scored two goals – the first time he has done so in the Premier League – in a remarkable second-half recovery from United as they won the Manchester derby 3-2 to deny City a win that would have seen Pep Guardiola’s men clinch the title.
It was a defiant response from Pogba, whose drop in form had seen him lose his starting place under Mourinho earlier this year, although his manager does not expect him to repeat such displays on a weekly basis.
Mourinho, however, has told Pogba he wants to see greater consistency from him, particularly in training, with the United manager clearly implying the 25-year-old midfielder has not always hit the necessary standards.
“I will tell you what I told him after the (City) match and it’s exactly what I told him – I don’t expect you to be man of the match every week, I don’t expect you to score two goals every week,” said Mourinho.
“I expect you to be consistent in a certain level. So, if you ask me, I’m expecting Paul now to be man of the match every week? No. If I expect him to score goals every match? No.
“But I expect Paul – and I think that’s the challenge he has to put to himself – to keep a certain stability and not to have the good match and the so-so match and the bad match,” the Portuguese boss added.
Pogba’s form, particularly since the January signing of Alexis Sanchez, has been one of the fascinating sub-plots of United’s season with the player reportedly unhappy at the defensive responsibilities he has been asked to perform.
Certainly, in a more advanced role, Pogba was devastating against City and Mourinho clearly believes his £89 million ($126 million) star is capable of repeating that form in the future.
“I think he has to try to keep that level of stability and from that stability of course will appear the special match with the special performance like it happened against City,” he said.
“But he has to go for that stability and to go for that stability, the first thing is stability at training level, stability during the working week. And the past two, three weeks I’m really happy with him.”
United’s strong recent form sees them take on West Bromwich Albion on Sunday looking for an eighth consecutive domestic victory and has raised optimism among supporters over their prospects for next season.
But, despite upsetting City at the Etihad last weekend, Mourinho has urged caution and clearly believes Guardiola will spend lavishly again this summer, while insisting United will not attempt to match his City counterpart’s outlay.
“No. We are not going to spend more than we can. We are not going to do anything crazy,” said Mourinho.
“We are just trying to improve a little bit more, to give sequence to it. That’s what we are going to try.”
Mourinho added: “I think Man City wins the title (this season). They have been the best team during the season and the distance of points at the end of the season will be the consequence of that superiority that they showed.
“But it is not about us and them, I think it is about the six teams. Everybody will try to improve like we did from last season.
“Last season we finished sixth and this season we are going to finish I believe fourth, third or second – hopefully second – and next season we are going to try and improve but let’s see what happens.
“Maybe also Manchester City will invest heavily and they don’t let the others close the gap to them, I don’t know.”
Pep Guardiola saluted his champions-elect for an “outstanding season” after they edged ever closer to the title.
Goals from Gabriel Jesus, Ilkay Gundogan and Raheem Sterling secured a 3-1 win at Tottenham and ensured the Premier League crown will be City’s in less than 24 hours if Manchester United lose to West Brom on Sunday.
Otherwise City have the chance to clinch the title at home by beating Swansea next Sunday.
Guardiola’s side arrived at Wembley on the back of three successive defeats, which saw them dumped out of the Champions League by Liverpool and miss the chance to seal the Premier League title by beating United.
But their response was emphatic and Guardiola said: “It was a good test against one of the toughest teams in the league.
“We now have 87 points with five games left because we have been outstanding all season.
“People say it was a big failure, what happened last week, but they don’t understand the reality of football.
“You can win the Champions League in seven games, the league is 10 months. I’m sorry, it’s much more important what these guys have done this season.
“Hopefully we can celebrate with our fans against Swansea and be champions because they deserve it.
“It’s one of the best by far. Winning titles in every league is important, with Barcelona was special.
“But the Premier League is one of the nicest and most important.”
Guardiola will not be watching United’s clash with West Brom, preferring instead to play golf with his son.
He added: “Will I hear the scores? Bogey, double-bogey, birdie.
“Of course, okay football is unpredictable. It doesn’t matter. It’s in our hands, we had one chance and now we have another.
“The players deserve all my respect for what they have done this season.”
Jesus struck in the 22nd minute when he raced onto Vincent Kompany’s 60-yard ball and fired home.
Gundogan scored the second from the penalty spot three minutes later after Spurs keeper Hugo Lloris brought down Sterling, although the contact was outside the penalty area.
Christian Eriksen pulled one back for Spurs before half-time but Sterling wrapped up the points in the second half.