MI defeated SRH by 13 runs despite posting a modest 150/5 on the board.
Opting to bat first, the defending champions posted 150/5 in 20 overs. Quinton de Kock was the top-scorer with 39-ball 40 while Kieron Pollard (35* off 22) and skipper Rohit Sharma (32 off 25) made notable contributions.
Vijay Shankar (2-19), Mujeeb Ur Rahman (2-29) and Khaleel Ahmed (1-24) starred with the ball for Sunrisers.
In response, however, MI bundled out SRH for 137 in 19.4 overs thanks to superb bowling performances from Rahul Chahar (3-19), Trent Boult (3-28) and Jasprit Bumrah (1-14).
"Great effort from the bowling unit, we knew it was not going to be easy. When you have a pitch like that and the bowlers execute, it makes it easy for a captain. I thought we had a good score for this pitch," Rohit said at the post-match presentation ceremony.
"You saw both the teams capitalizing on the powerplay. Having said that, we can do better in the middle overs. All the players are experienced enough to do that. But I don't want to take credit away from them, when you have guys like Rashid and Mujeeb bowling it's not easy," he added.
The MI captain Sharma also highlighted that the slowish nature of Chepauk pitch made it difficult for the batsmen to strike from the word go.
"The pitch is getting slower and slower, bowlers are always in the game till 20 overs. Even the seamers it's not easy to get them away and the slowish nature makes it harder for the batter to slog straight away," said Rohit.
"You need one set batsman at the end, just need some intelligent batting. I thought our fielding was good today, that's something we take pride in, we want to be the best unit in the tournament," he further remarked.
Mumbai Indians will take on Delhi Capitals in their next game on Tuesday (April 20).
(With ANI inputs)