Set an improbable target of 348 runs for an outright win, Delhi rode on Chand's unbeaten 106 and Gambhir's 51 to finish at 198 for no loss.
Chand struck 14 boundaries and one hit over the fence during his 154-ball knock while Gambhir hit only three fours during his 112 ball stay before retiring hurt, paving the way for Virender Sehwag to have valuable batting practice.
At stumps on the fourth and final day, Sehwag was other unbeaten batsman at the crease along with Chand.
Earlier, resuming at the overnight score of 198 for two, Mumbai declared their second innings at 347 for the loss of six wickets in 70 overs.
Also Read
Overnight batsmen Aditya Tare (122) and Siddesh Lad added seven and 25 runs to their yesterday's score.
Abhishek Nayar made a run-a-ball 60 which was studded with nine fours and one six.
For Delhi, left-arm pacer Pawan Suyal scalped three wickets for 52 runs.
Both Delhi and Mumbai garnered one point apiece from the fixture after both the teams were bowled out for identical 324 runs in their first essay.
Mumbai: 324 and 347/6 decl in 70 overs (Aditya Tare not 122, Siddesh Lad 85, Abhishek Nayar 60; Pawan Suyal 3/52).
Delhi: 324 and 198 for no loss in 48 overs (Unmukt Chand 106 not out, Gautam Gambhir 51).