Lokesh Rahul's unbeaten century and Chris Gayle, who scored 63, helped the visitors set a target of 197 for four.
However, thanks largely to a sensational 83 from Kieron Pollard in just 31 balls, the home side successfully chased down the total at 198 for seven.
Here are the standings after Wednesday's action:
IPL 2019 Standings
(Team, Played, Points, Net Run Rate)
1. Chennai Super Kings: 6, 10, +0.310
2. Kolkata Knight Riders: 6, 8, +0.614
5. Mumbai Indians: 6, 8, +0.290
3. Kings XI Punjab: 7, 8, -0.057
4. Sunrisers Hyderabad: 6, 6, +0.810
6. Delhi Capitals: 6, 6, +0.131
7. Rajasthan Royals: 5, 2, -0.848
8. Royal Challengers Bangalore: 6, 0, -1.453
1. David Warner (SRH): 349
2. Lokesh Rahul (KXIP): 317
3. Jonny Bairstow (SRH): 263
4. Andre Russell (KKR): 257
5. Chris Gayle (KXIP): 223
Thursday, April 11: RR vs. CSK
Friday, April 12: KKR vs. DC
Saturday, April 13: MI vs. RR, KXIP vs. RCB
Complete results, schedules and leaders available on the IPL's official website
Rahul took his maiden IPL century from 64 balls, smashing six sixes and as many fours along the way.
The 26-year-old adopted a relatively slow but steady pace throughout before producing an explosive finish with 36 from his last 12 balls.
Cricket pundit Harsha Bhogle was impressed:
The innings followed a 55 and a 71 from Rahul in Punjab's previous two matches:
Meanwhile, Gayle's knock of 63 came from 36 balls, including seven sixes.
His partnership with Rahul formed the bedrock of their 197 total, and the pair had reached 116 before Gayle was caught by Krunal Pandya in the 13th over.
Mumbai's task was difficult enough without coming up against a superb bowling performance from Mohammed Shami in the second innings.
The bowler grabbed three wickets—dismissing Siddhesh Lad, Hardik Pandya and Krunal Pandya—in four overs, giving up just 21 runs in the process.
However, Pollard led his side into contention with a superb performance that included 10 sixes.
Punjab finally stopped him in the final over when Ankit Rajpoot made a vital intervention:
It wasn't enough, however, as Alzarri Joseph and Rahul Chahar got the hosts over the line.