The touring side were closing in on victory and a 2-0 series triumph with Bangladesh just 95 runs ahead and only four wickets in hand. Skipper Shakib Al Hasan was 25 not out and nightwatchman Shafiul Islam unbeaten on nought.
Earlier, all-rounder Tim Bresnan compiled a Test-best 91 to lead England to a first-innings total of 496.
"Nine runs are nine runs, it's the contribution to the team that I'm more happy with," Bresnan said. "We've managed to get in front on a slow scoring wicket and I feel we've set it up perfectly for a win tomorrow," he said.
"I think four quick wickets tomorrow and we chase 150 and win, that's how I see it.
"We will be chasing a total I have a feeling about that, especially after getting the key wicket of Mushfiqur. We've got a nightwatchman in tomorrow and then Naeem, who'll hang in a bit, but if we can get them out we are sniffing a win," he added.
Bangladesh opener Tamim Iqbal blazed a half-centurybut no other top-order batsman made a big score.
SCORE BOARD
BANGLADESH (I Innings): 419 all out
ENGLAND (I Innings, 440/8 in 154 overs):
Bresnan st Rahim b Razzak 91
Tredwell st Rahim b Razzak 37
Finn (not out) 0
Total (all out) 496
Fall of wicket: 9-481.
Bowling: Shafiul 14-3-45-0, Razzak 39.3-8-132-3, Shakib 66-27-124-4, Mahmudullah 20-4-53-1, R Hossain 26-4-88-1, Naeem 7-0-29-0, Tamim Iqbal 1-0-4-0.
BANGLADESH (II Innings):
Tamim c Broad b Swann 52
Kayes b Broad 4
Siddique c&b Tredwell 34
Jahurul b Swann 43
Mahmudullah c Prior b Bresnan 6
Shakib (batting) 25
Rahim b Broad 3
Shafiul (batting) 0
Extras (W-5) 5
Total (for 6 wkts, 68 overs) 172
Fall of wickets: 1-23, 2-86, 3-110, 4-130, 5-156, 6-169.
Bowling: Broad 11-2-37-2, Bresnan 9-2-21-1, Tredwell 23-7-59-1, Finn 7-2-17-0, Swann 18-6-38-2.