Rishabh Pant hit a rapid half-century and Trent Boult held his nerve late as Glenn Maxwell's Delhi edged out fellow Australian D'Arcy Short's Rajasthan on the Duckworth/Lewis Method in the Indian Premier League.
Middle-order power hitter Maxwell could only contribute five runs for his side but Pant smashed 69 off 29 balls in Dehi's strong total of 6-196 in 17.1 overs before rain interrupted play for the second time.
Rajasthan's target was revised to 151 in 12 overs, but despite Jos Buttler's blistering 67 off 26 balls, Delhi hung on to restrict their opponents to 5-146.
Needing 15 runs off the last over, Boult conceded just one boundary and lifted Delhi from the bottom of the table to No.6 with six points.
"Really important win, coming in this situation, was a heart-throbbing match," Delhi captain Shreyas Iyer said.
"This wicket, here even 200 is less, but the bowlers kept their nerves and came back strong."
Rajasthan won the toss and opted to field after the match was reduced to 18-overs a side due to rain.
Captain Shreyas Iyer (50) and young Prithvi Shaw (47) laid a solid foundation with a 73-run second wicket stand after Colin Munro was dismissed for zero in the first over.
Pant then provided acceleration with his powerful hitting as he hit five sixes and seven boundaries and put on 92 runs with Iyer for the third-wicket stand off 43 balls.
Left-arm seamer Jaydev Unadkat (3-46) removed Pant and Iyer in the 15th over, but both batsmen had led Delhi toward a strong total.
Buttler gave Rajashtan a brisk start of 82 runs off just 40 deliveries in an electrifying run chase as the Englishman hit seven sixes and four boundaries.
But Rajasthan lost three quick wickets and lost the momentum after leg-spinner Amit Mishra outfoxed Buttler with a googly and Pant did a smart stumping.
Boult removed big hitters Sanju Samson (3) and Ben Stokes (1) while Short (44) was caught at short third man off Maxwell's offspin.
Rajasthan also has six points but is one place behind Delhi on net run-rate.
"Definitely disappointed. Buttler was amazing, but we could've batted better," Rajasthan captain Ajinkya Rahane said.
"We're still in the tournament ... all games are knockouts for us. It's all in the minds now. Character and attitude will be important."