Winger Mahrez ended a three-month Premier League goal drought at the Vitality Stadium by stepping off the bench to fire the champions back to the top of the table.
The Algeria international has made only 11 top-flight starts since his £60million switch to the Etihad Stadium last summer and been restricted to just 124 minutes of league action in 2019.
He was unexpectedly thrust into Saturday’s game during first-half stoppage due to an injury to Kevin De Bruyne and capitalised by securing a 1-0 success with a low finish in the 55th minute.
“It’s so important for him. Firstly, for the team,” said Guardiola.
“He has to be ready and positive – ‘OK, my time is going to come, the time is going to come’ – because there are a lot of games.
“I don’t have any doubts about his quality and always his mentality is aggressive.
“But he has to understand where he is and where he is is at a team who scored 100 points (last season) and in every single game fight and run and play.
“And the people in front are Leroy (Sane) – last season one of the most important players that we had – Bernardo (Silva), the best player in the league, and Raheem (Sterling).”
City enjoyed 82 per cent possession on the south coast and won having prevented Bournemouth registering a shot at goal.
The victory pushed Guardiola’s side two points clear of title rivals Liverpool ahead of Sunday’s Merseyside derby.
However, the success was tempered by De Bruyne’s hamstring injury and a recurrence of a groin problem for England defender John Stones.
Guardiola must wait to discover the extent of those problems but fears Belgium midfielder De Bruyne may be “out for a while”, although he said Stones was substituted as a “precaution”.
Mid-table Bournemouth saw their winless run to stretch to five games and have now been beaten home and away by both Liverpool and City.
Asked who he fancied for the title, Cherries boss Eddie Howe said: “Very difficult to call, I wouldn’t like to say one way or the other.
“I think they are different teams, different styles of play.
“But I think the common thing between both teams is they both have match-winners – at the right end of the pitch they’ve got those difference-makers.”
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Scott Parker believes the inquest into Fulham’s disastrous Premier League campaign must wait until May.
The Cottagers splashed out more than £100million on new players following promotion last summer but have since sacked two managers and appear condemned to an immediate return to the Championship.
Caretaker boss Parker has been tasked with bringing some stability back to Craven Cottage after replacing Claudio Ranieri on Thursday.
The 38-year-old inherits a team 10 points adrift of safety ahead of Sunday’s derby with west London rivals Chelsea.
“At the end of the season, whether you’re winning leagues or getting relegated, it’s a time to reflect and work out where the mistakes have been made and where you can improve things,” he said.
“There’s no denying, and it doesn’t lie, that the owners of this football club have invested an awful lot of money. Ultimately they have the club’s best interests at heart.
“I’m sure at the end of the season, when all the dust is settled, everyone will sit around a table and say ‘OK, look, this, this and this wasn’t good enough, this was perfect’.”
Parker, who was first-team coach under predecessors Slavisa Jokanovic and Ranieri, has 10 games in which to pull off an improbable great escape.
The former England midfielder acknowledges that the club’s position is perilous but wants his players to strive for survival until it is no longer mathematically possible.
Parker was relegated from the Premier League as a West Ham player in 2011 and admits the experience hurts.
“It does,” he said.
“It’s the same situation you find yourself in when you go into any club which is down at the bottom of the league. They’ll all have the same issues – confidence, whatever that may be.
“Certainly I’ve got experience from that as a player from being relegated. I’d like to learn from that and get that across to the players.”
The striker was a frustrated figure under former boss Claude Puel, admitting his tactics did not suit him.
The former England forward was also dropped by Puel on occasion, leading to a strained relationship, with Vardy apparently aiming a blast at the Frenchman when he was talking to Paul Pogba after a defeat to Manchester United.
But ahead of Sunday’s trip to Watford, Rodgers is ready to put Vardy at the top of the Foxes’ tree again.
“He is so natural at scoring,” Rodgers said. “When I see the team we need to get players closer to him.
"As a manager, it was my first job and it was always difficult for any team to go to Vicarage Road. We’ll expect a tough game, but I’m really looking forward to it."#WatLei— Leicester City (@LCFC) 2 March 2019
“The team has come deeper, the ball goes up to him and he’s fighting on his own.
“Because of the title win and everything around the threat of Jamie, space is no longer there all the time, especially at home. So when teams are banked up you have to find a way and a method that still exploits his qualities.
“It was something I spoke to him about at length on Friday morning before training, where we could get him into areas and how we were going to play against teams that just sit deep.”
Rodgers, who joined from Celtic on a three-and-a-half year deal on Tuesday, believes he will help develop nine-goal Vardy.
“I will certainly give him other ideas and just simplify the game,” he said.
“But you saw the other night (against Brighton) what he is – pass, makes the run and gets his finish.
“Away at Chelsea he comes in, (James) Maddison plays the pass, he makes a little blindside run and finishes.
“The problem is sometimes the gaps are a little bit too big and it’s just one long ball and he’s fighting for it.”
Luis Suarez scored 31 goals when Liverpool finished second in the Premier League under Rodgers in 2014, with the Northern Irishman keen to utilise Vardy in a similar way.
“You’ve got one of the best strikers who can press the game at the top end of the field so that’s where it starts,” he said.
“When I was at Liverpool it was Luis, he started the press so that’s where it begins. If you look at Manchester City, Tottenham and Liverpool, you’re not doing it for 90 minutes.
“Other times you’re just in and setting up the press to go and exploit the spaces.
“My teams have always been dominant about having the ball but having the ball to create opportunities. That’s always been the clear way of my work.”