Oldham defender Nathan Clarke scored on his debut to help the Latics to a second win of the season against 10-man Rochdale in the North West derby.
Dale went behind when Reuben Reid scored from the penalty spot after Chris Taylor went down under pressure.
Trotman was sent off for a second yellow before Clarke's diving header from Filipe Morais's corner put the hosts ahead on the stroke of half time.
Dale rallied after the break but could not find a gap against the extra man.
The Latics win lifts them to 13th in League One but leaves their opponents fourth bottom of the table with two points from four games.
The visitors started brightly at Boundary Park but Trotman received his first booking in the 28th minute for a foul on Reid.
Five minutes later Taylor won a weak penalty as Trotman closed in on him and former Dale loanee Reid scored past Jake Kean despite the keeper getting a hand to the ball.
A reckless challenge by Trotman on Kieran Lee in the 41st minute earned the Rochdale defender a second yellow card and gave Oldham the numerical advantage.
In the third minute of time added on at the end of the first half, Clarke - making his club debut on loan from Huddersfield - dived in to meet Morais's corner and sent a bullet header past the sprawling Kean.
After the break Marcus Holness twice came to Dale's rescue on the line as he stopped shots from Lee and Carl Winchester in quick succession.
Dale skipper Gary Jones came close with a shot over the bar and Nicky Adams flashed the ball across the face of the Latics' goal but the advancing Dale players could not turn the ball into the beckoning net.
VIEWS FROM THE DRESSING ROOM
Oldham manager Paul Dickov told BBC Radio Manchester:
"It's been a great three days, an away win at Scunthorpe and home win against your biggest rivals, we're all delighted.
"I asked them to go out and show me desire, commitment and a will to win and I got that.
"Last season we came up against 10 men a few times in the second half and we didn't go onto win the game, so it shows me they're learning as a group."
Rochdale manager Steve Eyre told BBC Radio Manchester:
"I thought we just edged the first 20-25 minutes and then it was a lack of discipline three times from one of our players, and it a real lack of game management for a 10-minute spell.
"We were in control of a game, but not leading it, and then you're staring down the barrel a little bit and waiting for a goal to go in, and it came with the penalty.
"We could have been looking at a bit of a drubbing second half, but the lads regrouped and showed incredible spirit and organisation, and at times we were better with 10 men."