Atletico Madrid remain three points behind as they were 1-0 winners at Getafe thanks to Fernando Torres's first minute goal. Real Madrid slip down to third, a further point adrift of Barca, who also have a game in hand on both clubs from the capital.
Messi's brilliant free-kick opened the scoring at the Camp Nou, but Celta deservedly drew level before half-time through John Guidetti's penalty.
However, Suarez took over in the final half hour as he swept home Messi's fine through ball and before prodding home from point-blank range.
"Some will like it, some won't, but as Barca players and members of the club, on top of winning titles, we try to enjoy our football in a spectacular way," said Barca boss Luis Enrique on Messi and Suarez's penalty trick.
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The final score was harsh on an under-strength Celta, who acquited themselves well for the first hour before being blown away by the magic of Barca's star front three.
Messi got a festival of brilliant goals started with a sumptuous free-kick from 25 yards into the top corner just before the half hour mark.
The Swede missed a spot-kick as Celta bowed out the Copa del Rey semi-finals against Sevilla in midweek, but the former Manchester City and Celtic striker dispatched the penalty confidently into the bottom corner.
Barca started much more brightly after the break and Suarez hit the post following brilliant wing play from Neymar just 60 seconds into the second-half.
The Uruguayan was more precise on the hour mark as he swept home Messi's scooped through ball first time into the top corner.
The party wasn't finished there as Suarez's lovely through ball was looped over Sergio Alvarez by Rakitic for the fifth.
And Suarez added another assist to a sparkling performance for Neymar also to dink the ball over the stranded Alvarez in stoppage time.
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.
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.
Elsewhere, Sevilla closed the gap on Villarreal in the battle for the fourth Champions League place to eight points with a 2-0 win over relegation threatened Las Palmas.
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.