Delhi lost the game by 48 runs after their batsmen could only manage 115 for nine in reply to Himachal's 163 for five.
Dhawan (12) failed for the second game in a row and it was a third failure for skipper Gamhbir (6) in as many innings.
Delhi had lost to Punjab yesterday after winning their opener against Jammu and Kashmir. They play Haryana in Dharamsala tomorrow.
They lost opener Prashant Chopra in the first over before Ankush Bains (23) and Paras Dogra (42) forged a 59-run stand. What followed later was the match winning partnership between Bipul Sharma (32 not out) and Rishi Dhawan (37 not out), who smashed 70 runs off 34 balls in their sixth wicket partnership.
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Delhi started their chase badly losing both Dhawan and Gambhir inside three overs.
The match was pretty much decided with Delhi reeling at 28 for five in the fifth over. Milind Kumar (31) and Pradeep Sangwan (24( tried their best to get Delhi back into the game but the damage had already been done.