Trott and Broad were able to rescue England from 102-7 with their lengthy partnership of 244, both ending the day unbeaten.
Earlier, Amir had become the youngest bowler to reach 50 wickets in Test cricket as he blew away the England middle order with Kevin Pietersen, Paul Collingwood and Eoin Morgan all departing without scoring.
This was the first time in EnglandÃ¢â‚¬â„¢s test history that numbers four to six have all failed to score during an innings.
Resuming the second day on 39-1, the Pakistani attack began perfectly as Alastair Cook, Pietersen and Collingwood were all removed without adding a run to the overnight score.
AmirÃ¢â‚¬â„¢s exceptional control was the highlight, leaving the majority of EnglandÃ¢â‚¬â„¢s batsman to edge helplessly to a grateful slip cordon who, today, took their chances.
However, Trott remained typically stubborn and his unflappable nature saw him prevail through a trying spell from Mohammad Asif and a verbal barrage from the Akmal brothers Kamran and Umar.
Broad built on his fine form from The Oval to offer vital support to Trott and bring up his maiden Test hundred late in the day. His aggressive innings, including 11 boundaries, eased the pressure on Trott who was therefore allowed to drop anchor.
England ended the day on 346-7, Trott unbeaten on 149 and Broad 125 not out. A dramatic turn-around now places the match momentum firmly with England despite such an appalling start.
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BIOGRAPHY: Ethan Hazard
BIOGRAPHY: Daniel Sturridge