Shaun Marsh, playing his first game this season, hit 65 to keep Kings XI Punjab in the hunt.
After Kings XI Punjab inserted Rajasthan Royals in Ahmedabad, Ajinkya Rahane played some enterprising shots at the start of his innings. He went on to make 74 off 54 balls.
Shane Watson, after a quiet start, played some powerful shots.
Following a 95-run opening stand with Rahane, Axar Patel got Watson stumped for 45.
Glenn Maxwell took two good catches on the boundary in a period that saw Rajasthan Royals lose quite a few wickets. The home team still managed to make 191/6.
Stand-in captain Virender Sehwag's run-out for 1 set the Kings XI Punjab chase back. Regular captain George Bailey didn't play on account of a shoulder injury.
David Miller, after being left out against Kolkata Knight Riders in the last match, played like a man possessed and scored his first fifty this season.
Axar Patel hit a four off the last ball to tie the score and take the encounter into the Super Over.
In the Super Over, Shaun Marsh took three fours off Chris Morris as Kings XI Punjab set a target of 16 runs.
Mitchell Johnson cleaned up Shane Watson off the first ball and then James Faulkner was run out off the third ball to hand Kings XI Punjab their second win of the season.