Dean Shiels handed the league leaders the opener after 13 minutes before Jon Daly nodded home his 20th goal of the season soon after.
But a wonder strike from veteran midfielder Steven Robb seven minutes after half-time set Light Blue nerves jangling.
And there was almost widespread panic in the later stages after Mohsni collected a second yellow card after booting the ball away at a Brechin free-kick.
Rangers kicked-off without Lewis Macleod as a persistent calf problem ruled the teenager out.
But manager Ally McCoist did still have Lee Wallace at his disposal after the cash-strapped Gers managed to stave off two Nottingham Forest bids before the January window closed.
After scraping to a 3-2 win against Arbroath last week, McCoist had demanded a better display but he got nothing like it.
The home side struggled last time out against the Hedgemen as they were forced to fight back from two goals down at Glebe Park in October to claim a 4-3 win.
This time they went in search of an early opening, only for Brechin keeper Graeme Smith - a former Rangers player - to twice deny them in the first five minutes as he saved from David Templeton and then Shiels.
The stopper's instinctive save down to his left to deny Daly's header from Templeton's cross from the left soon after was even more heroic.
But there was nothing Smith could do as Shiels collected the ball in the corner of the 18-yard box before bending a shot into the net to open the scoring.
And the keeper was just as blameless as the second goal arrived after 25 minutes. Darren Petrie's body check on Sebastien Faure handed Rangers a free-kick just outside the City box and from Wallace's teasing delivery Daly added a faint touch with his head to take it into the net.
But that was as good as it got for Rangers.
Mohsni collected the first booking with 10 minutes of the half left after a clumsy swipe felled Jonathan Brown, before referee Stevie O'Reilly flashed another yellow at Brechin right-back Paul McLean for a trip on Templeton.
Smith denied the hosts a third before the break as he blocked Fraser Aird's shot after a clever exchange involving Faure and Nicky Law put the winger through.
There was a casualness about Rangers' play as they returned for the second half which former St Mirren midfielder Robb exploited when he burst through the middle before ripping a stunning strike past Cammy Bell into the top corner to halve the deficit.
A low Wallace drive almost restored the Light Blues' two-goal lead but Smith was once more well-placed to push the full-back's effort out for a corner.
But just as Rangers should have gone up another gear, Mohsni put them back in trouble on the hour mark when he collected a second yellow for stupidly kicking the ball away after conceding a free-kick.
Despite their numerical disadvantage Rangers poured forward but saw Smith again deny Wallace and then Daly.
But the home fans were growing restless as their side toiled against part-time opponents and they let their feelings be known when Templeton managed to blaze over an open goal after Law drove to the by-line to feed Daly, who back-heeled the ball into his strike partner's path.
The groans only grew louder when Brechin substitute Robert Thomson only just missed finding striker Andy Jackson as he swept a low ball across Bell's goalmouth.
But Rangers managed to see out the nervy final five minutes to claim another unconvincing win which maintains their 23-point lead over Dunfermline.