The Catalans took the lead in the 28th minute as Lionel Messi curled in a brilliant free-kick before John Guidetti equalised from the penalty spot six minutes before the break.
Suarez gave Barca the lead just before the hour, finishing first time after Messi’s scooped pass, and he poked home his second with 15 minutes remaining following some lovely footwork from Neymar.
He completed his hat-trick after Messi had been brought down in the box. The Argentine passed up the chance to score his 300th La Liga goal, nudging the penalty a couple of yards forward and to his right allowing Suarez to run in and slot past a bewildered Sergio Alvarez in the Celta Vigo net.
The former Liverpool striker then turned provider, first setting up Ivan Rakitic and then Neymar for the fifth and sixth Barca goals.
The result takes Barcelona three points clear at the top of La Liga with a game in hand.
Elsewhere Atletico had a far more routine win at Getafe to remain in the title hunt.
Torres ended a five-month goal drought to net his 100th Atletico goal against Eibar last weekend and was brilliantly picked out by Yannick Carrasco’s low cross to get the visitors off to the perfect start.
Atletico then held on to record their 15th clean sheet in 24 Liga games this season to leapfrog Real Madrid back into second place.
However, Diego Simeone’s men did suffer a big injury blow when Carrasco hobbled off with ankle ligament damage early in the second period.
The Belgian international is now a major doubt for both Atletico’s trips to PSV Eindhoven in the Champions League last-16 next week and the Madrid derby in a fortnight.
In another match Sevilla closed the gap on Sevilla in the battle for the fourth Champions League place to eight points with a 2-0 win over relegation threatened Las Palmas.
Second-half goals from Ever Banega and Kevin Gameiro overcame the Canary Islanders’ resistance to register Sevilla’s 13th consecutive home win in all competitions.
Basque minnows Eibar’s brilliant second season in the top flight continued as they saw off Levante 2-0 to move up to sixth. And Real Sociedad moved into the top half with their third straight win 3-0 over Granada.