The veteran right-hander made 203 not out, his seventh double-century in 33 three-figure knocks, as the tourists piled up 730 for six declared on the third day at the Sher-e-Bangla stadium.
Having gained a mammoth lead of 498 runs, Sri Lanka reduced Bangladesh to 35 for one in nine overs before stumps to step closer to an overwhelming victory in the first match of the two-Test series.
Shamsur Rahman was unbeaten on nine and Marshall Ayub was on 11 at close, with Bangladesh still trailing by 463 runs.
Jayawardene, who now has 11,236 runs from 142 matches, equalled teammate Kumar Sangakkara’s Sri Lankan record of 33 Test centuries.
Jayawardene smashed 16 boundaries and four sixes in a typically elegant innings, as Kithuruwan Vithanage joined the run-spree with an unbeaten 103. Vithanage hit 12 fours and two sixes in his maiden century.
Sri Lankan captain Angelo Mathews partnered Jayawardene in a sixth-wicket stand of 179, himself making 86 before being dismissed before tea.
Jayawardene and Vithanage joined opener Kaushal Silva as the three century-makers in the innings, while Sangakkara, Dimuth Karunaratne and Mathews chipped in with half-centuries.
Left-arm spinner Shakib Al Hasan was Bangladesh’s most successful bowler with three wickets. But his 43 overs cost 159 runs.
The two-Test series will be followed by two Twenty20 matches and three One-Day Internationals.
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It was amusing to hear three "quicks" were used I watch the match at least in part. Didn't see any pace man .Do you consider 120 km as a pace bowing except as an occasional variant. They should watch m Johnson, steyn irfan . Now that is pace attack. What a sorry state of affairs for a team