This was Delhi's sixth win this season and they have 12 points now.
The hosts bowled well as Punjab managed 163/7.
Delhi then chased down the target with Shikhar Dhawan and Shreyas Iyer scoring fifties.
Here are the records broken.
Dhawan registers 35th career IPL fifty
Dhawan smashed his third fifty in IPL 2019. The senior cricketer also registered his 35th career fifty in the IPL. He surpassed Rohit Sharma in terms of IPL fifties (34) and needs one more to equal Gautam Gambhir, Suresh Raina and Virat Kohli (36 each).
Gayle surpasses 400 runs this season, smashes fourth fifty
Gayle also extended his IPL career sixes tally to 323.
The southpaw surpassed the 400-run mark this season (421).
He is only the second player to do so after David Warner (450).
Gayle smashes 28th career IPL fifty, Dhawan registers 500 fours
Gayle has now amassed 4,415 runs in the IPL.
He now has 28 career IPL fifties as well.
Dhawan became the first batsman in IPL to register 500 fours.
He needs nine sixes more to register a total of 100.
The opening batsman also became the first batsman to get past 300 runs for Delhi Capitals this season.
Delhi bowlers script impressive feats
Axar Patel (2/22) now has 67 career IPL scalps. Sandeep Lamichhane (3/40) registered his second best bowling figures in IPL. Purple Cap holder Kagiso Rabada (2/23) extended his tally to 21 wickets in IPL 2019.
DC vs KXIP
How did the match pan out?
For KXIP, no batsmen went on to support the veteran Gayle.
He played a lone hand as the side kept losing wickets.
After his dismissal, KXIP's innings got stalled.
R Ashwin and Harpreet Brar's cameos helped them get past 160.
In reply, DC lost Prithvi Shaw early on, but Dhawan and Shreyas Iyer took command and helped the side chase down the target.
Iyer registers 12th IPL fifty, surpasses 300 runs this season
Iyer (58*) smashed his second fifty in IPL 2019. This was also his 12th career IPL fifty. He became the second DC batsman after Dhawan to get past 300 runs in IPL 12.