Kavem Hodge struck an unbeaten 140 as West Indies moved to 345 for three in their second innings on the fourth day of the second Test against Bangladesh in Sylhet on Sunday, building a lead of 315 runs with a day to go.
The lead means Bangladesh will need the highest successful run chase in their Test history to win the match.
Their best remains 215, chased down against West Indies in 2009, and they have never won a Test chasing more than 200 on any other occasion.
West Indies scored 338 runs in 79 overs on Sunday and lost three wickets. Amir Jangoo, who made 133 in the first innings, was unbeaten on 20 at stumps alongside Hodge.
The visitors resumed on seven for no loss, 23 runs behind, and wiped out the deficit early. They scored 59 runs in the first hour without giving the Bangladesh bowlers a chance.
Taijul Islam made the first breakthrough, trapping Joshua Da Silva lbw for 36 with the score on 86. It was Taijul's first wicket since the second innings of the first Test in Mirpur.
Mehidy Hasan Miraz then removed Brandon King for 61. King pushed forward to a ball that drifted away from him, and the edge went to Najmul Hossain Shanto at slip.
King had made an unbeaten 81 in the second innings in Mirpur, and this was his sixth Test fifty.
West Indies scored 121 runs in 30 overs in the morning session and went to lunch on 128 for two, 98 runs ahead.
Hodge and Kevin Wickham then took the game away from Bangladesh. The pair added 131 runs in 28 overs in the afternoon session, and West Indies were 259 for two at tea.
Wickham, playing his debut Test, made his second fifty of the match off 68 balls. He became the eighth West Indies player to score two fifties on Test debut.
Hodge reached his third Test century by sweeping Taijul to fine leg. Taijul ended the stand soon afterwards, dismissing Wickham for 78. The pair had added 168 for the third wicket.
The pitch still offered little to the bowlers on the fourth day, and the West Indies batters kept scoring freely after tea.
Taijul finished the day with two for 118, while Miraz took one for 58.
Bangladesh made 386 in their first innings, led by Towhid Hridoy's unbeaten 242, the highest Test score by a Bangladesh batter. Left-arm spinner Jomel Warrican took four for 104.