The veteran right-hander was on 146 not out, his 33rd Test hundred, as the tourists went to tea on the third day at 602-6, a commanding lead of 370 over Bangladesh's first innings total of 232.
Jayawardene surpassed Allan Border's tally of 11,174 runs to move behind record-holder Sachin Tendulkar (15,921), Ricky Ponting, Jacques Kallis, Rahul Dravid, Brian Lara and Shivnarine Chanderpaul in the all-time list.
The 36-year-old, who now has 11,179 runs in 142 matches, equalled team-mate and close friend Kumar Sangakkara's Sri Lankan record of 33 Test centuries.
Bangladesh went wicketless for 50 overs after Sri Lanka resumed on 375-5 as the bowlers struggled to contain runs on the even-paced pitch.
Sri Lankan captain Angelo Mathews partnered Jayawardene in a sixth-wicket stand of 179, himself making 86 before being dismissed before tea.
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Mathews missed his third Test century when he mistimed a drive against spinner Sohag Gazi and was caught at short mid-on by Marshall Ayub.