Trott batted all day to reach 149 not out, adding 244 with Broad (125 not out) to lead England to 346 for seven in their first innings at the close of the second day. Broad, in an innings of genuine quality, scored his maiden Test century and the first by an England number nine since John Murray against West Indies in 1966.
His partnership with Trott is an England record for the eighth wicket against Pakistan, and the second highest against any country.
The hosts, 2-1 up in the series, were reduced to 47 for five in the morning session after resuming on 39 for one.
Eighteen-year-old Amir picked up six for 73 in 23 outstanding overs. He took four wickets in eight balls without conceding a run from the Pavilion end, dismissing Alastair Cook (10) and Kevin Pietersen (0) caught behind from consecutive deliveries.
Paul Collingwood was then trapped lbw for a duck and Eoin Morgan was smartly caught at second slip by Yasir Hameed, also without scoring. It was the first time the England number four, five and six had failed to score in a Test innings.
Amir became the youngest player to capture 50 Test wickets when Matt Prior was caught behind for 22 from the fourth delivery after lunch. Graeme Swann was then caught in the gully by Azhar Ali off Amir for yet another duck.
England, on 102 for seven, then staged a dramatic recovery through Trott and Broad.
Score Board
England (I innings, overnight 39-1)
Strauss b Mohammad Asif 13
Cook c Kamran Akmal b Amir 10
Trott (batting) 149
Pietersen c Kamran Akmal b Amir 0
Collingwood lbw Amir 0
Morgan c Hameed b Amir 0
Prior c Kamran Akmal b Amir 22
Swann c Azhar b Amir 0
Broad (not out) 125
Extras (LB-9, W-7, NB-11) 27
Total (for 7 wickets, 111 overs) 346
Fall of wickets: 1-31, 2-39, 3-39, 4-39, 5-47, 6-102, 7-102.
Bowling: Amir 23-5-73-6, Asif 26-6-83-1, Riaz 22-4-74-0, Ajmal 30-3-86-0, Hameed 1-1-0-0, Farhat 9-1-21-0.
