The Sri Lankan batsman hit eight fours to score 56 in 49 balls as Delhi made 5-140 in 19 overs after pace bowlers Umesh Yadav and Varun Aaron combined to take five wickets to help restrict Punjab to 6-136 at Ferozeshah Kotla Stadium.[break]
Jayawardene added 48 with Naman Ojha (34), helping Delhi recover from 4-37 in the sixth over.
Ojha struck three fours and two sixes in a 29-ball knock, both his sixes coming off successive deliveries from legspinner Piyush Chawla. He was dropped on 22 by Chawla at long-on off the bowling of Azhar Mahmood when Punjab were fighting to get back in the game.
Jayawardene guided the team to victory along with Irfan Pathan, who chipped in with 19 not out.
"There was some movement for fast bowlers and Varun and Umesh bowled beautifully," opener Virender Sehwag said.
"We were expecting that Mahela would play till the end and finish the game. It is difficult to go in and play your shots, but he took his time and ensured the win."
Earlier, Punjab captain David Hussey struck an unbeaten 40 but found little support from teammates.
In the playoffs: Delhi Daredevils batsman Mahela Jayawardene led the way with an unbeaten half-century against Kings XI Punjab overnight. Photo: AFP
Hussey, leading the side in place of compatriot Adam Gilchrist who has been out for most of the tournament due to a hamstring injury, struck one six and five fours in 35 balls.
In-form opener Mandeep Singh was the next highest scorer with 21 and one of Aaron´s two victims, the other being Shaun Marsh in a haul of 2-19.
But Yadav was the most successful bowler in claiming the wickets of Nitin Saini, Azhar Mahmood and Piyush Chawla to finish with 3-21.
Delhi have won 10 games and lost four. Kings XI Punjab have seven wins and seven losses and need to win both remaining games, against Delhi and Chennai Super Kings, to have a chance of qualifying.
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