India to a five-wicket win over Australia in the first ODI of the three-match series in Mohali on Friday.
Chasing a target of 277, Gill slammed 74 off 63 balls, while Gaikwad made 71 off 77 as India overhauled the target with eight balls to spare, reaching 281 for five.
Skipper KL Rahul (58 not out) and Suryakumar Yadav (50) also struck fifties each.
Earlier, in their first innings, Australia managed to score 276 runs, after Pacer Mohammed Shami got the second five-fer of his career to the visitors in check.
Australia started off on a shaky note as Mitch Marsh could not contribute much and departed in the very first over. David Warner and Steve Smith steadied the ship with a decent partnership.
And Warner went on to score fifty.
After Warner's wicket, Steve Smith failed to judge a deceptive delivery from Shami. Labuschagne's swift stumping added to Australia's woes, as India kept things under control and did not allow Australia's top order to dominate.
Josh Inglis played well to score 45 vital runs but was eventually outfoxed by a Bumrah's slower delivery.