Ashraful hit 136 with three sixes and 15 boundaries before he was removed by Muttiah Muralitharan.
The spinner ended with three for 85 and is just two wickets shy of 1,000 in international cricket.
After winning the toss, the hosts opted to bat at the Chittagong Divisional Stadium and looked ill at ease from the start of the two-test series.
Only one other batsman, opener Nafees Iqbal, scored more than 30.
Pace bowler Lasith Malinga took three wickets and Malinga Bandara two.