The late spark was provided by Bravo (23 off 8 balls) as CSK recovered from a disastrous start to put up a fighting total.
Chasing 157 on a pitch where the ball often stopped on the batsmen, MI too were off to a poor start as they slipped to 37 for three in the sixth over at the Dubai International Cricket Stadium.
Both Quinton de Kock (17) and debutant Anmolpreet Singh (16) got out after getting starts, the bowler being pacer Deepak Chahar on both occasions.
Suryakumar Yadav and Ishan Kishan too made their way back to the dugout in quick succession to leave MI in a spot of bother at 58 for four in the 10th over.
Saurabh Tiwary (50 not out) and stand-in skipper Kieron Pollard tried to forge a partnership before Josh Hazlewood had the big-hitting all-rounder from Trinidad trapped in front of the wicket.
CSK brightened their prospects further when Krunal Pandya was run out by the Dwayne Bravo-MS Dhoni combination.
Tiwary and Adam Milne tried but could not succeed, with the latter getting out to the experienced Bravo in the second ball of the 20th over.
Bravo picked up 3/25 while Chahar had 2/19 as MI ended at 136 for eight.
Earlier, the 24-year-old Gaikwad added 81 runs for the fifth wicket with Ravindra Jadeja (26) to steady the ship after they lost skipper Mahendra Singh Dhoni in the sixth over with the score reading 24 for 4.
Gaikwad smashed nine fours and three sixes, while Bravo hit three maximums as CSK scored 112 runs in the back 10.
CSK lost four wickets in the power play, including the wickets of skipper Dhoni and the team's seasoned run-getter Suresh Raina, as three top-order batsmen failed to open their account.
The start was inauspicious for CSK as Trent Boult dismissed Faf du Plessis in the fifth ball of the very first over when the New Zealand pace spearhead had the veteran South African caught by the backward point fielder Adam Milne, who was standing very fine, after the batsman had shaped himself up to play the cut shot.
One for one became two for two in the next over as Milne got Moeen Ali who slapped a slightly short ball straight to Saurabh Tiwary at cover.
What didn't help Moeen was that the ball seemed to stop as the England all-rounder went for his shot.
More trouble was in store for CSK as the three-time winners lost the big wicket of Raina in the third over when the experienced left-handed batsman, who has helped the team win so many matches in the past, got out to an irresponsible shot when he miscued one while trying to attack the Kiwi seamer.
Meanwhile, Ambati Rayudu retired hurt after taking a blow on his body to make matter worse for the Super Kings.
If that was not enough, holders Mumbai Indians piled more misery on CSK by sending the veteran Dhoni back to the hut for a poor score.
The World Cup-winning Indian captain timed his shot well but, to his shock, Boult completed a well-judged catch at deep square leg, capping a forgettable powerplay for the unit from Chennai.
After that, Gaikwad and Jadeja put together invaluable runs by mixing caution with aggression to give their team a total to defend against a side that is missing two of their big players in regular skipper Rohit Sharma and all-rounder Hardik Pandya, whose seam-up bowling was missed when the Chennai duo was rebuilding their innings.
Chennai Super Kings: 156 for 6 in 20 overs (R Gaikwad 88 not out, R Jadeja 26, D Bravo 23; A Milne 2/21, J Bumrah 2/33, T Boult 2/35).
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Morena, Jan 3: A Dalit woman and her daughter were brutally assaulted on Friday allegedly by two men and then dragged on the road in Morena in Madhya Pradesh following a minor incident involving a dog, a police official said.
A video of the incident, which took place in full public view in Ambah area, went viral on social media.
"Anita Mahor has sustained serious injuries after being hit by sticks and then dragged on the road. Her daughter Bharti is also injured. We have arrested Rajesh Tomar and Kumher Singh Tomar for assaulting them," Ambah police station in charge Satendra Singh Kushwaha said.
"Anita Mahor's son Deepak has told us that his younger brother Santosh was going to throw waste this morning when he was startled by the presence of a dog. He threw the waste, which also included dung, on the dog in fright and fled. This infuriated the two accused," he said.
The two accused and others stormed into Mahor's house armed with a chopper and sticks and attacked her and her kin, police said.