Englishman Buttler scored 97 not out off 54 balls for the Titans but never got a crack at his century in the last over, bowled by Australian pace ace Starc with 10 runs needed.
That was because teammate Rahul Tewatia smashed a six and a four off the first two balls.
Capitals star Starc conceded 49 runs, going wicketless from his 3.2 overs and was hit for five consecutive boundaries by Buttler in the 15th over.
Elsewhere, pacer Avesh Khan bowled a tremendous final over for Lucknow Super Giants to stun hosts Rajasthan Royals by a slender two runs in Jaipur.
Khan defended nine needed off six balls, conceding only six even as the drama was wound up by teammates dropping a catch and fumbling away a second run.
Rajasthan squandered a winning position from 2-156 after 17 overs and finished on 5-178 in reply to Lucknow's 5-180, powered by Aiden Markram and Ayush Badoni fifties.
Buttler missed out on a record-equalling eighth hundred as he hit 11 fours and four sixes to help complete Gujarat's chase with four balls to spare.
Sherfane Rutherford, 43 off 34, combined with Buttler for 119 off 69 for the third wicket — the stand underpinning Gujarat's 3-204 in 19.2 overs.
This was after Delhi Capitals made 8-203 led by skipper Axar Patel's 39 off 32.
Gujarat replaced Delhi on top of the table on run-rate.
Buttler reached 50 off 32 and picked up the scoring pace in Rutherford's company before the game took a sudden twist at the finish.
Rutherford was out caught in the penultimate over, leaving 10 needed off the last six deliveries. But Buttler was stranded on 97 when two big blows by Tewatia off Starc finished the match.
Earlier, Delhi struggled, especially against pacer Prasidh Krishna, who picked up 4-41 in four overs.
The best stand was between Axar Patel and Tristan Stubbs of 53 off 36. Ashutosh Sharma's cameo — 37 off 19 with three sixes — pushed Delhi across 200.
Opting to bat, Lucknow lost in-form Australian Mitchell Marsh (4) and tournament top-scorer Nicholas Pooran (11) early. Skipper Rishabh Pant fell for three and Lucknow slipped to 3-54 in 7.4 overs.
South African Markram scored 50 off 31, hitting three sixes and five fours, in his fourth half-century of the season. Badoni powered to 50 off 34.
Both perished in the space of 11 deliveries to leave Lucknow at 5-143, but Abdul Samad stepped in and smacked four sixes off the last four deliveries.
Rajasthan began their chase by debuting 14-year-old opener Vaibhav Suryavanshi, the youngest IPL cricketer. He didn't show any nerves, smacking his first ball for a six.
Suryavanshi scored 34 off 20 balls before he was stumped while fellow opener Yashasvi Jaiswal fired his fourth half-century, 74 off 52.
Jaiswal and Suryavanshi shared 85 off 52, then Jaiswal and stand-in skipper Riyan Parag added another 62 off 43 to have Rajasthan cruising.
Then Jaiswal and Parag fell to yorkers by Khan in the 18th over.
Khan bowled the final over as well, and took another wicket in a dramatic save.
- with AAP
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