Sri Lanka were 6-602 at tea on Wednesday’s third day of the first Test against Bangladesh at the Sher-e-Bangla stadium in Dhaka.
Mahela Jayawardene was unbeaten on 146, his 33rd Test century, as the tourists increased their lead to 370 runs with four first-innings wickets in hand.
Skipper Angelo Mathews made 86 and Kithuruwan Vithanage was unbeaten on 32.
Bangladesh failed to take a wicket in the morning session after Sri Lanka resumed on 5-375, as the bowlers struggled to contain runs on the even-paced pitch.
Bangladesh were dismissed for 232 in their first innings.
The two-Test series will be followed by two Twenty20 matches and three one-day internationals.