Zunaed Siddique and Mushfiqur Rahim delayed England's [ Images ] victory charge in the first Test with an unbroken 81-run stand to help Bangladesh score 191 for five in their second innings on Monday.
Zunaed eked out a patient half-century to remain 68 not out alongside Rahim (47 not out) at close on the fourth day.
The hosts are chasing 513 to win after England declared their second innings on 209 for seven.
Coming together around 20 minutes before the tea break, the pair batted out the entire final session to frustrate England.
"At no stage did we sit back and say we were going to finish this game today. We said we wanted to bowl as many dot balls as possible, build pressure on Bangladesh, and that will get us wickets," England pacer Steven Finn told reporters.
"They aren't going to be walked over because they've got good batsmen. We just wanted to bowl dot balls, good deliveries, and hopefully they'll get themselves out," he added.
Bresnan ended a stubborn 54-run third-wicket partnership when he had Aftab Ahmed caught by wicketkeeper Matt Prior [ Images ] for 26 and then bowled Mahmudullah for five.
Bangladesh suffered a huge blow when Shakib was given out leg before off Swann, with replays suggesting he got a full glove on his sweep shot.
Swann had earlier bowled Tamim Iqbal for 14 in his second over.
Imrul Kayes survived strong appeals for lbw and a catch at leg-gully before he finally edged Finn to Prior for 23.
"We already lost five wickets and their score is also very high. We will try to occupy the crease. If we can get a good partnership then the positives will come out hopefully," said Zunaed.
England, resuming on 131-5, lost overnight batsman Prior (seven) in the fourth over, but Ian Bell [ Images ] and Swann batted aggressively to help the tourists declare their second innings with an hour remaining in the first session.
England (1st innings): 599-6 declared (A. Cook 173, K. Pietersen 99, P. Collingwood 145, I. Bell 84)
Bangladesh (1st innings): 296 (T. Iqbal 86, Mahmudullah 51, M. Rahim 79; G. Swann 5-90)
England (2nd innings): 209-7 declared (S. Hasan 4-62)
Bangladesh (2nd innings):
T. Iqbal b Swann 14
I. Kayes c Prior b Finn 23
Z. Siddique not out 68
A. Ahmed c Prior b Bresnan 26
Mahmudullah b Bresnan 5
S. Hasan lbw Swann 4
M. Rahim not out 47.
Extras: (b-2, lb-2) 4
Total: (five wickets, 75 overs) 191
To bat: N. Islam, A. Razzak, R. Hossain, S. Hossain
Fall of wickets: 1-33, 2-45, 3-99, 4-105, 5-110.
Bowling: Broad 12-5-34-0, Bresnan 16-4-45-2, Finn 11-4-31-1, Swann 29-6-61-2, Pietersen 5-1-11-0, Trott 2-0-5-0.