Opening batsman Dhawan blazed 30 fours and seven huge sixes as he fell 20 runs short of the record held by Ali Brown, who bludgeoned 268 from 160 balls for Surrey against Glamorgan at The Oval in 2002.
The 27-year-old Dhawan also smashed 187 from 174 balls in his only career Test innings against Australia in March this year.
Another Indian batsman, Virender Sehwag, holds the record for the most runs in an official one-day international innings with 219 from 149 balls against West Indies in Indore in 2011.
India A ended their 50 overs on 433 for three wickets.
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