The home side took an early lead when Graham Hay headed home from a corner in the fourth minute.
Brechin doubled their advantage just six minutes later when Jonathan Brown lashed a 20-yard free kick into the top corner as Rangers struggled to get a foothold in the game.
In a feisty first half, no fewer than six players entered the book as Rangers looked for a way back into the contest.
McCulloch was made to pay for his miss when Trouten pounced on poor Rangers defending to restore his side's two-goal lead in the 35th minute.
It took Rangers just eight minutes of the second half to pull a goal back, as Bilel Mohsni got the deftest of touches on Nicky Black's free kick.
The comeback was complete in the 66th minute when Nicky Law's cross-cum-shot from the left flank evaded everyone and nestled into the corner of the net.
With the game approaching 90 minutes, Nicky Clark glanced home in the 85th minute to put his team ahead for the first time in the encounter.
Trouten picked up a second yellow card in the 90th minute as Brechin battled in vain for an equaliser.