Rahul (68) and his opposite number Hardik Pandya (66) both made quick half-centuries to prop up their respective innings in the low-scoring captains' duel.
Veteran Mohit Sharma took two wickets and facilitated two run-outs as the home side dramatically crashed in the final over on 128-7.
"I don't know how it happened, but it has happened. I can't put a finger on where it went wrong," a dumbfounded Rahul said afterwards.
Gujarat had opted to bat on a slow and low wicket and their 135-6 was testament to Pandya's sharp execution.
Shubman Gill was out for a duck off his second ball, but Pandya propelled Gujarat forward with four sixes before Marcus Stoinis sent him back in the final over.
Rahul started the chase slowly after earning the dubious distinction of becoming the first opener in IPL history to play out two first-over maidens in consecutive innings.
But he soon put paid to recent criticism of his strike rate, reaching his half-century off 38 balls.
The dismissal of fellow opener Kyle Mayers hit the brakes and Rahul failed to add to the eight boundaries he had already struck.
Only 18 runs followed off his next 23 balls, sucking the momentum out of Lucknow's innings despite a formidable 23 from Hardik's brother Krunal.
Rahul was still at the crease with 12 needed as the final over began but he was caught at square leg off the second ball.
Marcus Stoinis was out for a duck the next ball and Lucknow then suffered back-to-back run-outs as they slumped to defeat.
Punjab triumph
Punjab Kings triumphed in Mumbai with a hitting bout between the tournament's two most expensive players in near-perfect batting conditions.
Sam Curran steered the Kings to 214-8, with the Indians falling 13 short in reply.
Curran, who returned to Punjab for an eye-watering $2.23 million after December's player auction, hit a quickfire 55 off 29 balls with five fours and four sixes.
He had help from Harpreet Singh (41) and Jitesh Sharma (25) to give Punjab their highest score of the season, being dismissed when Jofra Archer took a return catch on the second-last over.
Cameron Green, Mumbai's $2.11 million man, made 67 off 43 balls in reply to keep the home side in the fight with help from Suryakumar Yadav's 57.
But Mumbai's brief window to come out on top was closed by left-armer Arshdeep Singh, who took Yadav and two other wickets in the final overs for match figures of 4-29.
