Having lost their first five matches, Delhi got off the mark with a win over Kolkata Knight Riders last week, and they followed it up with a seven-run success over Sunrisers.
The Capitals, despite strong contributions from Manish Pandey (34) and Axar Patel (34) failed to set an imposing total. Washington Sundar (3-28) helping Sunrisers restrict them to 144-9.
Sunrisers looked poised to canter to 145 when Mayank Agarwal (49) guided them to 69-1. However, they subsequently lost four wickets for 16 runs, leaving Heinrich Klaasen (31) and Sundar (24 not out) to lead a recovery mission.
Though Klaasen fell with nine balls remaining, Sundar was in a position to get them over the line, Sunrisers needing 13 off the last.
But Mukesh Kumar did not allow a single boundary in the final six balls, frustrating Sunrisers with superb death blowing to seal triumph for Delhi.
Delhi celebrate new low
The Capitals' total of 144 is the lowest they have successfully defended in the IPL. Their previous best in that regard came back in 2009, when they prevailed against Rajasthan Royals when defending 150.
Bhuvneshwar brilliance not enough
Bhuvneshwar Kumar will feel aggrieved to be on the losing side. The Sunrisers seamer bowled 16 dot balls in his four overs, the most by any bowler this season. His 11 runs conceded also marked the lowest total by any bowler to complete his allocation of overs in the 2023 campaign.
A stingy innings in the field from the hosts was followed by an excellent knock from Devon Conway, who smashed 77 from 57 balls to give CSK their fourth win of the season.
Harry Brook (18) was the first to fall for Sunrisers after he made room for himself and attempted a big hit, only to slice it behind for Ruturaj Gaikwad to make a superb low catch.
Abhishek Sharma (34) and Rahul Tripathi (21) looked to be building a nice partnership before the both ballooned shots into the air for simple catches off the bowling of the impressive Ravindra Jadeja.
Captain Aiden Markram (12) did not have long at the crease with South Africa team-mate Heinrich Klaasen as he edged Maheesh Theekshana to Mahendra Singh Dhoni, with the wicketkeeper also stumping Mayank Agarwal (2) soon after as Sunrisers fell from 71-1 to 95-5.
While they were able to stem the tide of wickets, Sunrisers struggled to find runs as CSK's bowlers kept their opponents on a leash, ultimately rewarded when Klaasen (17) fell to Matheesha Pathirana as Gaikwad snaffled another catch.
Marco Jansen (17 not out) and Washington Sundar (9) played out the remainder of the innings, with the latter being run out from the final ball as the Sunrisers scored just 37 from their last 36 balls to end on 134-7.
An opening partnership of 87 from the first 11 overs put CSK in control of the chase, before Gaikwad was run out by Umran Malik on 35.
Ajinkya Rahane (9) was dismissed by Mayank Markande, who also bowled Ambati Rayudu (9) with a superb delivery, but Conway and Moeen Ali (6 not out) eased their team home with eight balls to spare.
Conway shows the way
Sunrisers Hyderabad have still not won an IPL game against CSK at MA Chidambaram Stadium, losing all four, and Conway made sure that remained the case.
The New Zealand international hit 12 fours as he set about extinguishing any hopes the visitors had of ending that run, and recorded his third consecutive half-century, making him just the third CSK player to do so after Gaikwad and Faf Du Plessis.
Jadeja shines with the ball
Jadeja really did some damage with the ball, taking three wickets and conceding just one boundary from his four overs.
His figures of 3-22 were the fourth three-wicket haul from him in an IPL game on this ground, tied for the second-most by any bowler at the venue (behind Albie Morkel with 5).
Warner issued a rallying cry to the Capitals' top order on Wednesday with the franchise in danger of missing out on a spot in the next round.
And it was as if he felt the need to lead by example as he produced a stellar showing, hitting 92 not out to break the record for most T20 half-centuries in history as the Capitals set a significant target of 207-3.
It was just as well Warner was so sharp as the Capitals endured a difficult start when fellow opener Mandeep Singh was removed for a duck by Bhuvneshwar Kumar (1-25) on the fifth ball – Mitchell Marsh (10) did not last much longer.
Captain Rishabh Pant proved a reasonable partner to Warner with 26 off 16 balls before falling to Shreyas Gopal (1-34), but that would prove to be the final Capitals wicket to tumble.
Rovman Powell (67 not out) and Warner put on a stand of 122 as the Capitals surpassed 200, with Umran Malik (0-52) and Kartik Tyagi (0-37) in particular toiled with the ball.
Sunrisers' chase did not start especially well as Abhishek Sharma and Kane Williamson put on just 11 between them – Rahul Tripathi at least managed double that figure, but they needed more.
Aiden Markram (42) and Nicholas Pooran (62) at least offered some resistance with their 60-run stand, but hope dissolved after the former skied a delivery from the excellent Khaleel Ahmed (3-30) into the hands of Kuldeep Yadav.
Although Pooran managed to reach his half-century, no one else added more than 10 as Sunrisers fell well short at 186-8.
Warner makes history
This was Warner's fourth half-century of the season and comfortably his biggest total (by 26 runs), but the focus was on his new record as he surpassed Chris Gayle (88) for the most 50s in T20 cricket.
After managing a disappointing three last time out, Warner's display here was a timely response against his former team. His haul came from just 58 balls and included 15 boundaries, three of which were maximums. Warner certainly did not do it all himself, as Powell's contribution was significant, but it was some showing.
All pace no precision?
Malik recorded the second-fastest ball in IPL history in the 20th over of the Capitals' innings, the delivery clocking 157 kilometres per hour. But, in general, he did not enjoy a great day.
The Capitals totalled 52 runs against him, more than any other bowler, and he did not claim a single wicket.