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Sehwag grabbed four wickets for six runs with his off-spin as Bangladesh were shot out for 167 in 34.5 overs after losing their last six batsmen for the addition of just 12 runs.
India cantered past the modest target in the 31st over, with Sehwag's Delhi team-mate Gautam Gambhir smashing 82 off 101 balls with the help of six boundaries.
Sehwag managed only 11 with the bat and Bangladesh captain Shakib Al Hasan removed Virat Kohli and Rohit Sharma off successive balls, but India were never in trouble.
Skipper Mahendra Singh Dhoni (38 not out) put on a match-winning stand of 78 with Gambhir, who fell leg-before to Mashrafe Mortaza when just 10 runs remained for victory.
Defending champions Sri Lanka had opened the four-nation tournament on Tuesday with a 16-run win over Pakistan.
Each team plays the other once in the league with the top two advancing to the final on June 24.
Bangladesh, who elected to bat after winning the toss, made a flying start as openers Tamim Iqbal and Imrul Kayes hammered 35 from the first 17 deliveries.
After Tamim fell for 22 off 12 balls, caught in the covers off Praveen Kumar, Kayes and Mohammad Ashraful added 46 for the second wicket.
Bangladesh were 81-1 in the 14th over before three wickets fell for 19 runs, two of them to seamer Ashish Nehra who removed Kayes (37) and Ashraful.
Mushfiqur Rahim (30) and Mohammad Mahmudullah (23) put on 55 for the fifth wicket, before India dented the innings.
Sehwag, who missed the World Twenty20 in the Caribbean due to a shoulder injury, marked his return with a superb spell on the slow wicket at the Rangiri stadium.
He had Rahim caught at the wicket, trapped Suhrawadi Shuvo and Shafiul Islam leg-before and then terminated the innings by bowling last man Syed Rasel.
Sri Lanka take on Bangladesh in the next match on Friday.
