Sediqullah Atal smashed his maiden century but Mehidy Hasan Miraz struck twice to expose Afghanistan’s tail as the Abu Dhabi Test moved into the final session.
The hosts reached 265-5 at tea with Sediqullah batting on 105 from 299, with Yamin Ahmadzai keeping him company.
Hashmatullah Shahidi, who came back after retiring hurt earlier, fell on the stroke of the tea-break, leaving Afghanistan a mountain to climb. Miraz earlier removed Ismat Alam, who was caught behind for a 60-ball four runs.
Chasing a massive target of 479, Afghanistan resumed the session on 203-4 with Sediqullah and Ismat at the crease.
Sediqullah survived a stumping chance as Litton failed to grab the ball on the first attempt off the bowling of Taijul, which was Bangladesh wicketkeeper’s first mistake of the match.
Ismat took all the time before getting off on the 45th delivery he faced.
Sediqullah then became the first Afghan batter to hit a century in the fourth innings of a Test match, when he pulled Hasan Mahmud for a four. He played 277 balls to complete the milestone, which was also his maiden first first-class hundred.
Ismat fell soon after Sediqullah’s hundred, as his outside-edge ricocheted off Litton’s pad before it was grabbed by Shanto who was backtracking.
Just when Afghanistan seemed to drag the Test into the final session with five wickets remaining, Hashmatullah had a brainfade moment.
The former captain tried to charge Miraz and was caught at mid-on by Hasan, just seven minutes before the scheduled tea-break. He made 36 off 69.
Having started the day with 347 runs still needed with seven wickets remaining, Afghanistan chose to rearguard with Sediqullah the main warrior.
Bangladesh managed a solitary wicket in the first session, courtesy of Litton’s record-breaking diving catch.
Ikram Alikhil was strangled down the leg side by Ebadot, who was throwing a short ball barrage. This was Litton’s ninth dismissal of the match, becoming the first wicketkeeper in the history of Test cricket to make nine dismissals while scoring at least a hundred and a fifty in the same match.
The previous best combination belonged to South Africa’s Denis Lindsay, who scored 69 and 182 and took eight dismissals against Australia in Johannesburg in 1966. Litton, with 53 in the first innings and 102 in the second, has now gone one better.
There was, however, a half chance early in the morning when a catch of Sediqullah fell just short of Tanzid Hasan at silly point.
Sediqullah, meanwhile, reached his maiden fifty in Test cricket in 166 deliveries, having begun the day on 35.