Trott, Morgan push England to 225
The 24-year-old Morgan, drafted in the team as a replacement for Kevin Pietersen, hit eight fours en route to his 63 off 72 balls, while Trott scored 67 off 99 balls with two fours at the Zahur Ahmed Chowdhury Stadium here.
The duo forged a 132-ball 109-run fourth-wicket stand to lift England to 162 in 38.4 overs after being reduced to 53 for three early in their innings.
England, however, lost their way, suffering another collapse in the face of a disciplined Bangladeshi bowling and lost their last six wickets for just 63 runs.
Naeem Islam, Abdur Razzak and skipper Shakib Al Hasan accounted for two wickets each, while Rubel Hossain, Shafiul Islam and Mohammad Mahmudullah got one apiece.
Sent into bat, wicketkeeper batsman Matt Prior walked out with skipper Andrew Strauss to open the England innings and combined for a 32-run partnership before losing his wicket in a bizarre fashion in the seventh over.
Strauss, too, was dismissed in the 11th over with Junaid Siddique taking a brilliant catch at slip off Naeem Islam. A lot was expected of Ian Bell but the right-handed batsman became Mohammad Mahmudullah`s victim as England slipped to 53-3 in 16.4 overs.
However, Trott and Morgan steadied the ship, adding 109 runs to lift England to 162.
The duo shrugged extravagance and toiled hard on the field, taking singles and twos to keep the scoreboard ticking.
Morgan, who is returning from an injury, picked up his first boundary in the 21st over when he lofted Mahmudullah over mid-wicket, before welcoming skipper Shakib Al Hasan with a boundary over mid-off.
The left-handed batsman showed excellent footwork and sent Mahmudullah for another four over midwicket, before pulling him along the carpet for another boundary.
Trott picked his first boundary in the 28th over off Rubel Hossain, bisecting the fine leg and deep square boundary. Morgan, meanwhile, swept Islam for another four, before using his feet to good result against Rubel.
In the 35th over, Morgan brought up his fifty with a single off Shafiul Islam, while Trott cantered to his individual half-century in the next over.
However, Naeem Islam brought Bangladesh back into the game, removing Morgan in the 39th over with Imrul Kayes taking a brilliant diving catch running in from deep fine leg.
After the 41st over, England took their batting powerplay but couldn`t utilise the five overs. With pressure mounting, Trott went for a big shot and holed out at long off to trigger another collapse.
Graeme Swann and Paul Collingwood took England across the 200-mark but, in pursuit of quick runs, wickets kept tumbling, as Bangladesh held things back in the end.