A game billed as the clash between Indian superstars Virat Kohli and M.S. Dhoni saw 33 sixes hit in Bengaluru.
Devon Conway and Shivam Dube blasted 83 and 52 respectively to help Chennai post a commanding 226-6 batting first.
But Bangalore skipper Du Plessis (62) and Maxwell (76) brought the home crowd alive in a blazing partnership of 126.
The pair tore into the opposition attack, striking 12 sixes between them after losing two early wickets including Kohli for six in the first over.
Dhoni played his part with two high catches to dismiss the dangerous pair, with Maxwell and Du Plessis falling in the space of two overs.
Sri Lankan mystery spinner Maheesh Theekshana removed Maxwell after his 36-ball blitz, including eight hits over the boundary, and England spinner Moeen Ali sent back Du Plessis.
Dinesh Karthik attempted to keep up the attack with his 14-ball 28 but Chennai regained control with regular wickets as Bangalore failed to keep up with the asking rate.
With 19 runs needed to win from the final over, Matheesha Pathirana, a fast bowler with a slinging action, kept his calm to give away just 10.
See the full scorecard on Flashscore.
Conway set the tone for the match with his 45-ball knock, laced with six sixes, as he put on big partnerships with Ajinkya Rahane and then Dube.
Rahane smashed 37 before being bowled by Sri Lankan spinner Wanindu Hasaranga but Conway kept up the charge with Dube for company in a partnership of 80 off 37 balls.
Bangalore attempted to pull things back with the wickets of Conway and Dube, who departed after a 27-ball innings.
But Moeen steered the team to the mammoth total with his unbeaten nine-ball 19.
