The Sanju Samson-led side have moved into fifth position with a 4-wicket win.
The Capitals won by 15 runs despite Liam Livingstone's fighting 94.
The win took PBKS to 12 points from as many games, just outside the top four, while it was the end of the road for DC.
Rinku Singh scored the winning runs to secure a 5-wicket win for KKR.
Suryakumar smashed 66 off 31 balls, while opener Kishan scored 75 off 41 balls.
Raza sent the final ball towards the boundary but Theekshana stopped it just before the ropes in a brilliant fielding effort but by that time the Punjab batters had completed three runs to silence the home crowd at Chepauk.
Marcus Stoinis scored a 72 as the Super Giants posted 257/5.
The left-arm pacer's heroics earned him plaudits from both Punjab skipper Sam Curran and Rohit Sharma, Mumbai and national captain.
In a high-scoring match at the Wankhede, the visitors won by 13 runs.
PBKS were bowled out for 150 in 18.2 overs in their chase of 175.