Pujara, playing his first match of the season, and Gayle shared a 102-run stand to give their side a rollicking start and AB de Villers came up with a 38-run cameo off just 19 balls towards the end to propel the side to a huge score.
Gayle's 61 came off 33 balls with nine boundaries, including three sixes, while Pujara scored 51 off 48 balls and helped himself with eight shots to the fence.
Manpreet Gony dismissed bowled both Gayle and Pujara and the visitors lost skipper Virat Kohli (14) cheaply after that but de Villiers ensured that the good start does not go waste as he blasted his way to 38 with four fours and two sixes.
He collected 21 runs off the final over, bowled by debutant Michael Neser along with Moises Henriques.
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As if the Gayle bashing was not enough, Pujara too got into the act, scoring a hat-trick of boundaries off Gony in the next over as Bangalore raced to 58 for none in six overs.
Even Gayle's mis-hits were kissing the boundary ropes as he raced to his half-century in 27 balls.
Gony returned and was hoicked for a six by Gayle but he had his revenge when he uprooted Gayle's stumps in the next ball. That wicket did affect the run-rate even as skipper Kohli and Pujara took the side to 133 for one in 15 overs.