Rohit, the only batsman to hit three double hundreds in the 50-over format, added 165 with fellow opener Lokesh Rahul to power India to 260-5 in their 20 overs for the joint-highest total by a team in what is the shortest format of the game.
In reply, Sri Lanka, who lost the opening match by 93 runs at Cuttack on Wednesday, were bundled out for 172 in the 18th over to go down 2-0 in the three-match series after also losing in tests and one-day internationals.
India's wrist spinners once again did the damage for the hosts with leg-spinner Yuzvendra Chahal taking 4-52 while left-armer Kuldeep Yadav picked up 3-52.
Angelo Mathews could not bat due to an injury as Sri Lanka's chase screeched to a halt after they lost six wickets in two overs from the spinners.
Kusal Perera top-scored with 77 off 37 balls for the touring side, who had also gone down 9-0 across formats to India at home earlier in the year.
The 30-year-old Rohit smashed 10 sixes and 12 fours before he was eventually dismissed for 118 in 43 balls on a featherbed of a wicket at the Holkar Cricket Stadium, where Sri Lanka captain Thisara Perera won the toss and opted to field.
Four of Rohit's sixes came in consecutive deliveries off Thisara which took him to 97 and he completed his second hundred in the format with a four on the next ball he faced from seamer Angelo Mathews.
Rahul took charge after Rohit's dismissal and added 78 for the second wicket with former captain Mahendra Singh Dhoni before falling for 89 off 49 balls.
India were well on course to eclipse the highest T20 International total of 263-3, which was set by Australia against Sri Lanka in 2016, but lost their way by losing four wickets in the last two overs of their innings.
Mumbai's Wankhede Stadium will host the final match of the tour on Sunday.
(Reporting by Sudipto Ganguly in Mumbai and Shrivathsa Sridhar in Bengaluru; Editing by Keith Weir/Jeremy Gaunt)
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