Dhawan retired hurt for 60 after being hit by a short ball from rookie left-arm seamer Atif Sheikh, the only blip for the tourists on their way to a teatime 214 for two which also featured a half-century for Gautam Gambhir (54).
Both left-handers walked off with 50s under their belts, Gambhir merely retiring himself out and Dhawan conversely leaving the fray to some general consternation - although initial indications were he had not sustained a serious injury.
That apart, all went smoothly for India at the start of this three-day match, which lost its scheduled first-class status after the hosts agreed to the tourists' request to play as many of their 18-man squad as they choose.
India will bat only 11, however, against opponents who were in fruitless action against Surrey at The Oval the previous day but nominated only four of those beaten in London to see out a week-long marathon of cricket here.
Leicestershire are bottom of LV= County Championship Division Two, without a win in nine matches this season, and fielding a second-string side it was little surprise they were unable to tame India's Test top order.
On a pitch tinged with green and offering decent carry, after India won the toss, Dhawan escaped on nought and went on to prosper on a sunny morning for a 79-ball 50 which contained 10 fours.
In the first over of the match from Anthony Ireland, Dan Redfern was unable to hold on to a sharp head-high chance offered to third slip.
Instead, India had 46 on the board before Leicestershire managed a first breakthrough - Murali Vijay aiming a drive towards mid on and edging some full-length swing from Ireland to gully.
Dhawan reached his half-century shortly before lunch but was bounced out of the action in the early afternoon by a delivery that appeared to perhaps not quite make the expected height and hit him near his elbow.
Twenty-three-year-old Sheikh worked up some useful pace from the Bennett End in a spell which belied a career record featuring just one previous first-class appearance to date, for Derbyshire against Gloucestershire back in May 2010.
Gambhir, joined by Cheteshwar Pujara, passed his 50 in 95 balls and shortly afterwards decided he had done enough - vacating the crease to allow Virat Kohli his turn for some match practice.
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