Ivan Rakitic, Lionel Messi, Marc Bartra and Neymar were also on target as Barca reasserted their control on the Spanish title race.
Victory moved Barca back three points ahead of Atletico Madrid and four clear of third-placed Real Madrid with both sides from the capital in action later on Wednesday against Athletic Bilbao and Villarreal respectively.
Barca had taken just one point from their last possible 12 in the league and been dumped out of the Champions League amidst a run of just one win in six games that threatened to derail their season.
However, they remain in control of their own fate and few would bet against them winning their last four games and claiming a 24th Liga title after a performance as good as any in the 39-game unbeaten run they enjoyed prior to losing at home to Real Madrid earlier his month.
Suarez settled the visitors’ nerves after just 11 minutes when he outmuscled Sidnei to volley home the opener despite the hosts’ desperate appeals for a foul.
Borges then had an even better opportunity as he rounded Bravo, but Bartra got back to block his effort from point-blank range before Oriol Riera fired the follow-up over.
Suarez gave Barca the cushion they desired when he latched onto Messi’s sumptuous through ball to slot low past Manu.
The Uruguayan should have had a first-half hat-trick but he failed to turn home Alves’s fine cross from two yards out moments later.
Suarez made amends as he turned provider for Barca’s third just after the break when his cross to the back post was volleyed home emphatically by Rakitic.
Messi created the fourth with another defence splitting pass and Suarez kept his composure to seal his sixth hat-trick of a prolific season.
The relief amongst the Barca players was palpable as they seemed to click back into the form that had them set for a second consecutive treble before their sudden collapse in the previous six games.
Suarez was gifted his fourth of the night from Neymar’s unselfish cross despite Laure blocking his initial attempt on the line for his 49th goal of the season.
The former Liverpool striker then added a second assist to his four-goal haul as Barca again tore the Deportivo defence apart and his cut-back was gratefully tapped home by Messi.
Bartra joined the party as he galloped forward from his own half without facing a single strong Deportivo challenge before firing into the far corner.
And Neymar completed a perfect night for the Spanish champions when he tapped home at the far post from Suarez’s third assist of a spectacular display for his first goal in six games.
Diego Simeone has hinted he thinks Barcelona will drop more points this season.
Atletico have won their last three league games, as well as knocking Barca out of the Champions League, to move level with the Blaugrana at the top of the table.
And although the Catalan club hold the head-to-head advantage, Atletico know that one more slip-up from Luis Enrique’s side will open the door for them to become champions for the second time in three seasons.
Simeone said: “I’m not a prophet, and it’s very difficult to predict what will happen. But I have the feeling we don’t depend on anybody else. We depend upon ourselves. I’m just saying what I think.”
However, the question of whether Atletico will be able to win all five of their remaining fixtures is another matter, with Wednesday night’s trip to Athletic Bilbao presenting Simeone’s men with one of their toughest tests of the season.
A good run of form has lifted the Basque club into fifth place in the table, and they have lost just one of their last 13 league games at San Mames.
Simeone, who will be without suspended skipper Gabi for Wednesday night’s contest, said: “Athletic are an important team with a lot of strength all over the pitch. But we are ready. We aren’t doing any tactical work because all the boys already know exactly what to do and they are all ready to play.”
Considering their consistent excellence over the last three years, it is no great surprise to see Atletico Madrid standing shoulder to shoulder with Barcelona and Real Madrid in La Liga’s title race.
But the identity of the man who is spearheading their challenge certainly comes as a major shock to the system.
Just a few weeks ago, Fernando Torres was effectively on the scrapheap with his career apparently in irreversible decline. Seemingly unwanted by boss Diego Simeone, he couldn’t even break into the team despite the struggles endured by big-money summer signing Jackson Martinez, and the question of when he would score his 100th goal for Atletico had become a running joke.
Torres reached 99 in a victory over Eibar in September and then, like a nervous batsman on the verge of his maiden Test match century, he got stuck there. For weeks, and weeks.
Eventually, nearly five months later, another meeting with Eibar saw Torres finally break into double figures, and the celebrations that followed among Atletico fans had a sentimental, nostalgic feel, as though they were marking the postscript to the outstanding career of one of their favourite sons.
Since then, however, Torres has enjoyed arguably one of the most spectacular and unexpected renaissances in recent sporting history.
A week after netting his 100th goal, he scored again – a winner at Getafe. Then he got another, giving his team the lead in a 3-1 victory over Valencia which helped seal Gary Neville’s fate at Mestalla.
And now, crazily, Torres just can’t stop, with his classily taken effort in Sunday’s 3-0 home win over Granada marking the first time he has scored in four consecutive games since 2010.
They aren’t just any old goals, either – they are vital strikes for a team which is competing for two of the most prestigious trophies in the world: an equaliser which led to victory at Espanyol, the opener in a home win over Real Betis and, most significantly, a drilled strike against Barcelona which eventually secured passage into the last four of the Champions League.
From being a national joke, he is now being talked about – seriously – as a potential late call-up for Spain’s European Championships squad to solve national coach Vicente Del Bosque’s biggest dilemma: a reliable striker.
For a player who last represented his country nearly two years ago in the disastrous 2014 World Cup campaign and whose international career was widely assumed to be over, the fact he is even being mentioned is a remarkable turnaround.
The former Liverpool and Chelsea striker’s revival tells us a lot about his attitude – the never-say-die spirit which made him such a popular figure with Atletico fans when he first broke into the team as a teenager all those years ago.
It also tells us a lot about Simeone’s ability to extract the utmost out of the players at his disposal. If players are prepared to work hard and buy into his system (Martinez being an example of one who didn’t), Simeone has that knack of making them better than anyone ever thought they could be.
A look at some of the decidedly ordinary players who became Spanish champions with Atletico two years ago (Diego, Adrian, Jose Sosa, Cristian Rodriguez) is enough to prove that point, and Torres is benefitting in the same way.
Now, the striker’s long-term future appears to be safe – his loan deal from AC Milan expires at the end of the season and, until recently, Atletico did not appear to be inclined to keep him. But that has all changed, and a permanent deal is expected to be agreed in the coming weeks.
First, though, he has other things on his mind: trophies. And the way things are going, we shouldn’t rule out the prospect of Torres completing his fairytale comeback by scoring an injury time winner against Real Madrid in the Champions League final.