Gujarat needed 11 runs from the final over and Deshpande conceded only four for Rajasthan's second win from two matches, ensuring they lead the table on net run-rate from Delhi Capitals, who beat Mumbai Indians earlier on Saturday.
Rajasthan notched 6-210 thanks to Dhruv Jurel's 75 off 42 balls and Yashasvi Jaiswal's 55 off 36, while 15-year-old opener Vaibhav Sooryavanshi scored 31 off 18.
Gujarat, on the back of Sai Sudharsan's 73 off 44 and tailenders Rashid Khan (24) and Kagiso Rabada (23no), mounted a terrific comeback to reduce the chase to a reachable 15 off the last 12 balls.
But Jofra Archer allowed only four runs in the 19th over before Deshpande closed the last over with two dot balls and Khan's wicket to leave Gujarat stranded at 8-204.
Earlier, Delhi beat Mumbai by six wickets in the national capital and went top of the table for approximately four hours.
Sameer Rizvi blew away Mumbai with 90 runs off 51 balls to help set up Delhi's second win.
The impact player followed his unbeaten 70 against Lucknow SuperGiants on Wednesday with seven sixes and seven boundaries in his highest IPL score.
Delhi raced to 4-164 and a six-wicket win with 11 balls to spare in reply to Mumbai's 6-162, delivering a first loss for the five-time champions.
Rizvi came in with Delhi in trouble at 7-2 in the second over, joining opener Pathum Nissanka, who was the initial aggressor in their 66-run stand.
When Nissanka top-edged a pull straight up on 44 at 3-73, Rizvi took charge of the chase at Arun Jaitley Stadium.
Rizvi's 50 off 31 balls led Delhi to 100 in the 12th over. He appeared set for his maiden IPL hundred and was 10 runs away when he went looking for his eighth six and was caught at long-off in the 17th over.
"Rizvi never let us get back into the game," Mumbai stand-in skipper Suryakumar Yadav said.
Eariler Mukesh Kumar (2-26) struck twice for the Capitals in the third over, bagging Ryan Rickelton (9) and taking a return catch from Tilak Varma for a two-ball duck.
Yadav and Rohit Sharma combined for 53 off 40 balls but the slowish Delhi pitch didn't allow the Mumbai stars to run away.
Delhi skipper Axar Patel got the breakthrough when Sharma slapped him to cover and Nitish Rana took a tough chance in the 10th over.
Yadav got 51 off 36 but was out lbw to Lungi Ngidi and Mumbai faded thereafter.
