After the opening game of the five-match series in Canberra was washed out on Wednesday night, Australia went 1-0 up with a commanding performance.
With the huge crowd in Melbourne made up predominantly of Indian fans, Hazlewood silenced them from the beginning after captain Mitch Marsh won another toss and elected to bowl first.
After dismissing India for 125 off 18.4 overs, Marsh (46) and fellow opener Travis Head (28) went about trying to end the match as quickly as possible, with Australia chasing down India's disappointing target with a whopping 40 balls to spare, racing to 6-126 off 13.2 overs.
Marsh, who has been in scintillating white-ball form, smashed one of the biggest ever sixes at the MCG when he blasted Harshit Rana into the second level of the Olympic Stand.
After whacking four sixes, Marsh went for one big shot too many and was caught at long off with Australia 39 runs away from victory.
Australia lost 4-39 after Marsh's dismissal, which included Jasprit Bumrah getting on a hat-trick, but were never in any danger of losing the match.
Hazlewood never relented after seemingly taking a wicket with the first ball of the match, which was then overturned on review, to finish with figures of 3-13.
Opener Abhishek Sharma batted superbly, playing a lone hand to save India from embarrassment with 68 from 37 balls.
Sharma didn't manage to find enough of the strike, however, for India to truly capitalise on his class.
Allrounder Harshit Rana (35 from 33 balls), who came to the crease in the eighth over at No.7, only faced four less deliveries than Sharma.
Hazlewood's night could have been better, with wicketkeeper Josh Inglis dropping a catch and Shubman Gill successfully challenging an lbw dismissal.
The pro-Indian crowd were jubilant early as Sharma was able to take Xavier Bartlett for 17 from the second over.
But Hazlewood's lethal line and length shocked India, reducing the tourists to 4-32 from five overs.
The 34-year-old's second over ended with two wickets and just one run.
When allrounder Axar Patel was run out in sloppy circumstances to slump to 5-49, India's hopes of building a competitive total were all but shot.
Bartlett (2-39) recovered from a challenging start, dismissing Rana and Shivam Dube.
But Sharma was again able to get hold of the Queenslander, with 17 runs coming off his fourth and final over.
Nathan Ellis also bowled well, finishing with figures of 2-21.
A tribute for teenage cricketer Ben Austin, who tragically died after being struck by a ball while batting in the nets on Tuesday afternoon in Ferntree Gully in Melbourne's east, took place before the game.
Both teams and officials observed a minute's silence for Ben.
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