Kumar Sangakkara and Mahela Jayawardene compiled another mammoth partnership as Sri Lanka closed at 500-4 on day three in Kandy, 369 ahead of Bangladesh.
The prolific pair, who shared an epic 624 against South Africa in Colombo last year, put on 311 after joining forces in the 21st over.
Left-hander Sangakkara was unbeaten on 222, his second successive double century, striking 28 fours.
Skipper Jayawardene, seeking to seal a 3-0 whitewash, hit three sixes in 165.
Resuming on 30-0, Sri Lanka suffered an early setback when Upul Tharanga misjudged one that angled in from Syed Rasel and offered no stroke.
Sangakkara got off the mark in fine style, clipping his fourth delivery through the gap between mid-wicket and mid-on to the boundary.
Michael Vandort had just steered his seventh four when Rasel nipped another delivery back and it crept between bat and pad, on to leg-stump.
Jayawardene hit two fours in three deliveries from Mashrafe Mortaza and pulled a short delivery from Shahadat Hossain in front of mid-wicket for six.
The captain was first to three figures, reaching his 18th Test century in the 61st over with a delicate dab for two.
His partner recorded his 14th century two overs later slamming Mohammad Ashraful off the back foot through the covers for four.
Jayawardene reached his next milestone, the 150, by cutting a short, wide delivery outside the off-stump from Shahadat Hossain over the ropes for six, but having coasted to 165 he tried to hit over the top and caught it high on the bat, the ball looping to mid-off.
When Sangakkara had made 188 he offered a sharp return catch to Mohammad Ashraful and although the spinner could not hold it, his deflection ran out Chamara Silva at the non-striker's end.
The fluent Warwickshire batsman was pleased to receive a full toss on leg-stump when he was on 198 and duly pulled it to the square-leg fence to record his sixth Test double century.
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