Jayawardene's double ton floors Bangladesh
Mahela Jayawardene (right) plays a shot as Mushfiqur Rahim (left) looks on during the third day of the first Test match between Bangladesh and Sri Lanka at the The Sher-e-Bangla National Cricket Stadium in Dhaka - by Munir Uz Zaman
The veteran right-hander made 203 not out, his seventh double-century in 33 three-figure knocks, as the tourists piled up 730-6 declared on the third day at the Sher-e-Bangla stadium.
Having gained a mammoth lead of 498 runs, Sri Lanka reduced Bangladesh to 35-1 in nine overs before stumps to step closer to an overwhelming victory in the first match of the two-Test series.
Left-arm spinner Rangana Herath, brought on after three overs, struck with his third delivery when he forced Tamim Iqbal to mistime a catch to point.
Shamsur Rahman was unbeaten on nine and Marshall Ayub was on 11 at close, with Bangladesh still trailing by 463 runs.
Jayawardene leapfrogged Allan Border (11,174 runs) and Shivnarine Chanderpaul (11,219) to move behind record-holder Sachin Tendulkar, Ricky Ponting, Jacques Kallis, Rahul Dravid and Brian Lara in the all-time list.
The 36-year-old former captain, who now has 11,236 runs in 142 matches, equalled team-mate and close friend Kumar Sangakkara's Sri Lankan record of 33 Test centuries.
Jayawardene smashed 16 boundaries and four sixes in a typically elegant innings, reaching 203 with a six over mid-wicket off Nasir Hossain.
Kithuruwan Vithanage joined the run-spree with an unbeaten 103 as Bangladesh conceded their highest ever total, surpassing the 648-9 by the West Indies in Khulna in November 2012.
Vithanage, a 22-year-old left-hander playing his third Test, hit 12 fours and two sixes in his maiden century.
Bangladesh struggled to contain the runs on the even-paced wicket after Sri Lanka resumed the day on 375-5.
Sri Lankan captain Angelo Mathews partnered Jayawardene in a sixth-wicket stand of 179, himself making 86 before being dismissed before tea.
Mathews missed his third century when he mistimed a drive against spinner Sohag Gazi and was caught at short mid-on by Marshall Ayub.
That turned out to be Bangladesh's lone success in the day as Vithanage helped Jayawardene add 176 for the seventh wicket, before Mathews closed the innings.
The only time Jayawardene appeared in trouble was when he survived a loud appeal for leg-before on 119 as he attempted to reverse-sweep Sohag Gazi.
Television replays favoured the bowler, but the Decision Review System is not being used in the series.
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.
Al-Amin Hossain had one for 118 in 32 overs, while fellow seamer Robiul conceded 109 runs in 29 wicketless overs.
The two-Test series will be followed by two Twenty20 matches and three one-day internationals.