Sri Lanka finished day four of the first Test on 176-3 after being set a mammoth 453 to win by West Indies in Trinidad.
Kusal Mendis reached the close unbeaten on 94 as the tourists fought back with the bat, albeit they still require a further 277 runs to clinch an improbable victory.
Angelo Mathews (31) and Roshen Silva (14) shared in half-century partnerships with opener Mendis, who hit two sixes and nine fours to move within sight of a fifth Test ton.
However, West Indies struck twice in the final session and with Dinesh Chandimal forced to retire due to illness, they remain the most likely winners.
Earlier, Kieran Powell missed out on reaching three figures before the home team - who opted not to enforce the follow-on - cut short their second innings on 223-7.
Having resumed on 64 not out, Powell added a further 24 runs before he fell trying to lift Dilruwan Perera over the top, his attempt only providing a catch to midwicket.
Skipper Jason Holder contributed 39 from 40 deliveries as West Indies picked up the pace, leading to a declaration early in the afternoon session.
Yet their pacemen struggled to have the same impact as the first innings, allowing Sri Lanka to dig in and leave the series opener nicely poised going into Sunday's play.