Dhananjaya de Silva and Kamindu Mendis both slammed their second century of the match as Sri Lanka set up a 511-run target for Bangladesh before pushing the hosts to the corner in the first Test on March 24.
The visitors were all out for 418 in their second innings at Sylhet, with Mendis making 164 runs to go with his 102 in the first innings and De Silva, who also scored 102 runs in the first innings, adding 108.
Sri Lankan pacers began the victory push immediately, reducing Bangladesh to 47-5 at stumps, with 464 more needed for an unlikely win.
