Sri Lanka now trail by 218 runs, with de Silva (170) and Mendis (125) out in the middle.
Pace bowler Mustafizur Rahman earlier broke Mendis's 308-run second wicket stand with de Silva, who added 69 runs to his overnight 104. "I don't think it is the way to bat in this wicket".
Roshen Silva (82 not out) and captain Dinesh Chandimal (37no) also cashed in on a flat track to take Sri Lanka on to 504-3 in reply to Bangladesh's 513 all out on Friday.
De Silva led Sri Lanka's batting charge with his aggressive approach and brought his fourth Test hundred off 122 balls with a cover drive off left-arm spinner Taijul Islam.
In the last nine Tests Bangladesh played at home and away, the only instance where they could score more runs in their second innings was in Potchefstroom against South Africa - 172 in the second innings compared to 147 in the first innings and they lost by 254 run.
Despite dismissing Dhananjaya, Mendis and Silva continued to punish Bangladesh as they put together a 107-run partnership, during which Mendis found himself within touching distance of his maiden double hundred.
De Silva survived a strong leg before wicket appeal on 119 off Taijul Islam when the ball hit him on his toe before going to the slips. "There are rough areas that are created as bowlers bowl from different angles". Sri Lanka's wily left-arm spinner Rangana Herath will definitely bowl most of the overs alongside an accurate right-arm pace bowler Suranga Lakmal and slow left-arm chinaman Lakshn Sandakan. "Rough can sometimes make a bad ball into a good one".