Joining opener Akash Chopra (62 not out; 207m, 165b, 8x4) in the first wicket, Gambhir struck a crackling 126 (153m, 111b, 25x4, 1x6) to build a 170-run partnership and pave way for an eight-wicket victory for the visitors.
Chopra played the anchor while the team India opener toyed with Bengal bowling to enable Delhi reach their second innings target of 222 in just 49.5 overs, wrapping up the game shortly before tea.
Earlier, Delhi pacers Lal and Bhandari created havoc in the Bengal second innings as the hosts, who resumed at 190/3, managed to add only 42 runs to their overnight total to be all out for 232 in less than an hour's play this morning.
Lal (4/72) and Bhandari (5/61) bowled unchanged for 11.3 overs that the Bengal batters could survive. Bhandari, who had scalped five in the previous innings as well, had a match haul of 10 wickets for 116 runs.
The tourists' bagged four points for their first outright victory this season to increase their tally to 12 points from six matches, thus brightening their semifinal prospects.
Bengal, on the other hand, remained on four points from six games, facing relegation risks after conceding back-to-back defeats in four outings.
Brief score: Bengal 240 and 232 Delhi 251 and 222/2 (G Gambhir 126, A Chopra not out 62).