Shashank Singh's 61 and a late cameo by debutant Ashutosh Sharma saw Punjab reach the target of 200 with one ball to spare, the highest successful chase this season.
"Still trying to sink in," said Singh.
"Visualised all these things, but when it turned into reality, proud of the effort."
For most of the evening, Gujarat looked on course for a comfortable victory with Punjab plummeting to 70-4 in the ninth over. Captain Shikhar Dhawan was out in the second over when he chopped one onto the stumps.
England batsman Johnny Bairstow fell soon after for 22, deceived by Afghan spinner Noor Ahmad who was the pick of the Gujarat bowlers with 2-32. Young wicketkeeper Prabhsimran Singh scored an entertaining 35 off 24 balls but holed out trying to pick up the pace.
Singh came to the crease with Punjab still needing 130 runs but made 61 off 29 balls, with six fours and four sixes. Impact substitute Sharma, playing his first-ever IPL match, chipped in with a quick 31 off 17 balls to pull off an unlikely win for the Kings.
Gujarat skipper Gill batted through the home team's innings to score 89 off 48 balls, the highest individual score this season.
New Zealand captain Kane Williamson scored 26 in his first appearance this IPL season for Gujarat after opener Wriddhiman Saha fell cheaply for 11. Gill and left-hander Sai Sudarshan stitched together a rapid partnership of 53 in the middle overs to give Gujarat a launching pad to accelerate in the final overs.
All-rounder Rahul Tewatia provided the final fillip with a quickfire 23 off eight balls - together he and Gill raked in 56 runs in the last four overs to take Gujarat to 199-4.
Gill blamed the defeat on "dropped catches".
"Never easy on a wicket like this," he added.
