The home side were scrapping to hold a 2-1 lead just short of half-time when Trollope reacted badly to a free-kick given against his striker Andy Williams.
Prolonged protests to the assistant brought the referee over and as Trollope continued to complain he was ordered from the technical area.
Tensions had been building during a three-goal spell in four minutes, which had seen Forest already pull back a goal on ambitious Rovers.
That came when Byron Anthony knocked the ball into his own net.
To rub it in, the cross for it came from Rovers' old favourite Junior Agogo, who left them for Forest in an acrimonious transfer a year ago.
Grant Holt brought Forest level in added-on time to the first half and they must have fancied their chances of going on to win.
It is 16 years since these clubs last met and two trademark free-kicks by Kris Commons gave the visitors an early edge.
But they were to play out the last ten minutes a man short when Holt collected a second card - the first for kicking the ball away and the second for a misjudged tackle.
From Rovers' first strike on 25 minutes, when Anthony put away a piercing through ball from Chris Carruthers, the tempo hardly slackened.
Two minutes later they doubled their lead as a foul in the box by Luke Chambers brought home striker Richard Walker his first goal this season with an accurate shot to the left of keeper Paul Smith.
The Forest keeper twice suffered clearance aberrations when he put the ball straight to an opponent, but each time he got away with it in this highly competitive game.