A dogged stand of 59 from 36.4 overs between Dhawan (55 not out) and Parida (52) ensured the home side did not get bowled out as they ended at 186 for 7 in 88 overs on the fourth and final day at HPCA Stadium.
Since the first innings for both sides remained unfinished due to the weather, each team got a point each.
Andhra extended their overnight score from 301 for 6 to 336 for 8 declared, before Himachal's top order was rocked by seamer Paidikalva Vijaykumar (3/47).
Brief Scores:
Andhra: 336 for 8 decl in 97 overs (Murumulla Sriram 105)
Himachal Pradesh: 186 for 7 in 88 overs (Rishi Dhawan 55 not out, Rashmi Parida 52).