Left-handed opener Sudharsan smashed 82 off 53 balls -- his third half-century of the season -- and spearheaded Gujarat to 6-217 after Rajasthan won the toss and bowled on Wednesday.
Right-arm fast bowler Krishna then picked up 3-24 in four overs with his sharp, short deliveries and spinner Rashid Khan took 2-37 as Rajasthan were bowled out for 159 in 19.2 overs.
Shimron Hetmyer of the West Indies top-scored in the chase with 52 off 32 balls and captain Sanju Samson made a 28-ball 41, but both fell to Krishna, who impressed with the old and new ball.
Gujarat have eight points with four wins in five games.
They fell short by 11 runs in their only loss against Punjab Kings in the opening game run-fest at home.
Gujarat have a two-point lead over second-placed Delhi Capitals, who have played two fewer games. Delhi, having won all three of their games, are the only unbeaten team in the tournament.
Rajasthan, who came into the game on the back of successive wins against Chennai Super Kings and Punjab, are seventh after five matches.
Arshad Khan and Mohammed Siraj took the sting out of Rajasthan's run-chase inside the first three overs when they dismissed Yashasvi Jaiswal and Nitish Rana cheaply.
Jaiswal timed the ball confidently, only to see Rashid not moving an inch at third man for the catch, and Rana's ramp shot flew to Kulwant Khejroliya, also at third man, as Rajasthan slipped to 2-12.
Samson and Riyan Parag (26) revived the chase briefly with Parag smashing three sixes before he was dismissed by impact player Khejroliya, thanks to a successful Gujarat review.
Earlier, Sudharsan continued his sublime form, laying the foundation for the win when he and Jos Buttler put on an 80-run, second-wicket stand.
That came after captain Shubman Gill (2) had his off-stump clattered by Jofra Archer's 147kph (91 mph) delivery.
Buttler, who moved to Gujarat after playing seven IPL seasons for Rajasthan, made 36 off 25 balls.
Sudharsan kept Gujarat going at more than 10 an over by smashing three sixes and eight fours but missed out on a century, eventually was caught behind off a thin inside edge against Tushar Deshpande (2-53) in the penultimate over.
