Former captain Jayawardene (203 not out) hit off-spinner Nasir Hossain for two sixes in the same over to reach the double century before running off the ground as Sri Lanka immediately declared their innings.
On a day of batting milestones, Jayawardene (11236) overtook former Australia captain Allan Border (11174) and West Indies left-hander Shivnarine Chanderpaul (11219) to climb up to sixth on the list of highest test run-getters.
Vithanage (103 not out), playing his third test, reached the 100-mark in 99 deliveries as the Bangladesh bowlers failed to make any impact on a docile batting pitch.
The duo added 176 runs for the unbroken seventh wicket.
The tourists resumed on 375 for five and captain Angelo Mathews (86) was the lone Sri Lankan wicket to fall on Wednesday, dismissed by off-spinner Sohag Gazi.
Mathews added 179 runs for the sixth wicket with Jayawardene, who remained not out after a 272-ball knock studded with 16 fours and four sixes.
(Writing by Sudipto Ganguly; editing by Amlan Chakraborty)
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