The ex-Thistle co-manager, recruited from Dundee, made an immediate impact, providing the through ball that split the Clyde defence to allow Steven Hampshire clear in the inside-left channel to slide the ball low past Jarvie for a dream start.
That was in the fourth minute, and 60 seconds later, Britton spurned the chance of instant success by tamely side-footing Ally Mitchell's lovely cross against the goalkeeper.
Clyde should have drawn level on the quarter hour mark, Stephen O'Donnell opening up the home defence down the left, his pull-back blazed wide by Alex Williams from close to the penalty spot. Five minutes later, Gary Bollan was booked for a crude foul on Craig Bryson, and, from the resultant free-kick by skipper Paul McHale, Chris Higgins headed just over with Craig Nelson beaten.
Just before the interval, Hampshire missed from close range - failure to convert scoring opportunities has been Brechin's Achilles heel thus far this season - and in injury time, Steven Hamilton saved bravely from a goal-bound shot from Clyde's Stephen O'Donnell. The opening half was completed with Clyde assistant manager Joe Miller being sent-off for uttering oaths that could have been heard down in the town's cathedral.
The second half began like the first, with a goal, and it was a personal disaster for Nelson, who allowed an innocuous 20-yard shot from McHale to slip through his legs and over his line for as soft a goal as the good people of Brechin will see all season.
Clyde almost took the lead 10 minutes into the second period; with the home defence stretched following a quick throw by Williams, O'Donnell drove the ball against the base of Nelson's left-hand post with the goalkeeper comprehensively beaten.
And on the hour, Clyde deserved to take the lead after a delightful one-two between Bryson and Alex Williams, but Nelson made amends for his earlier blunder.
Two minutes later, Clyde's Neil McGregor was sent-off along with Britton after an unnecessary altercation with the ball already out of play, the pair squaring-up after Clyde defender Eddie Malone had been knocked over.
Ten-a-side and a rash of substitutions fractured the flow of play, although two replacements, Brechin's Charlie King and Clyde's Roddy Hunter, had late chances to take all three points and Nelson saved Brechin's bacon on the stroke of full-time with a finger-tip save from Bryson.
The Scotsman
GERRY BRITTON was sent packing on his Brechin debut as Clyde came from behind to stretch their unbeaten run to six games.
The ex-Partick Thistle boss went in hard and late on Bully Wee full-back Eddie Malone in 61 minutes and was then pushed to the ground by Neil McGregor, giving referee Mike Ritchie no option but to give both players their marching orders.
Brechin grabbed the opener after five minutes through Steven Hampshire and Britton was instrumental in the build-up.
The former Partick Thistle boss collected the ball from Steven Ferguson at the edge of the penalty box and sent a perfect pass to the unmarked Hampshire who netted easily from five yards.
Clyde had a great chance to level after 17 minutes when Stephen O'Donnell's cross picked out Alex Williams in the area but the striker sent his effort past the post when it seemed easier to score.
The visitors looked set to score again ten minutes later when Michael McGowan rifled in a shot from 18 yards but Steven Hamilton made a great goal-line clearance.
City should have extended their lead in 37 minutes when a Darren Smith pass created an opening for Hampshire but the striker ballooned over from a good position.
Clyde assistant boss Joe Miller was sent to the stand by referee Ritchie just before the break after he said something to the stand-side linesman.
Paul McHale snatched the leveller within a minute of the restart. The Bully Wee skipper picked up a clearance from Scott Walker 30 yards out and fired past Craig Nelson who got a hand to the shot but couldn't stop it finding the net.
The visitors had a chance to take the lead seven minutes later when O'Donnell latched on to a loose ball in the middle of the park and let fly from 30 yards but his shot hit Nelson's left-hand post and was cleared.
Clyde looked more at ease after they were reduced to 10 men than the hosts and they passed up a great chance to bag the winner nine minutes from the end when Malone crossed into the box for Roddy Hunter but he headed past from just a yard out.'
www.iclanarkshire.co.uk
A great reverse pass by Brechin City's new home signing, the experienced Gerry Britton, set up Stevie Hampshire for a fourth minute opener for the Angus side. Britton collected the ball from new colleague Steven Ferguson at the edge of the penalty box to set up his unmarked striking partner Hampshire who netted easily from five yards.
Clyde had a great chance to equalise in the seventeenth minute when a Stephen O'Donnell cross was cut back to Alex Williams in the area but the former Morton striker sent his effort past the post when it seemed easier to score.
Ten minutes later Michael McGowan hit a shot from eighteen yards but Steven Hamilton made a great goal-line clearance to maintain his team's lead. That lead was nearly doubled just before the interval when scorer Hampshire's powerful effort was nullified thanks to a tremendous stop by Paul Jarvie.
Despite long periods when Clyde were in control it remained 1-0 for City until half time. At times in the opening period the game threatened to get out of control, none more so than during a seven minute period midway through the half when three Brechin players were booked.
Less than sixty seconds after the resumption, a Clyde corner headed out of the box by the home defence arrived at the feet of Clyde captain Paul McHale, whose powerful twenty-five yard shot went through a mass of bodies but somehow eluded the normally reliable Craig Nelson in the City goal to give Clyde a well deserved if slightly fortunate equaliser.
For the next quarter of an hour Clyde's superiority was not reflected in any more goals. Then in the sixty-first minute both teams were reduced to ten men when Clyde's Neil McGregor and City debutant Gerry Britton were sent off. The dismissals were sparked off when Gerry Britton, apparently trying to stop the ball going for a goal kick, went in hard, and late, on Eddie Malone. The ex-Partick Thistle co-manager was then pushed to the ground by Neil McGregor who over-reacted to the Britton-Malone incident, leaving referee Mike Ritchie with no option but to send off both players.
Thereafter it was Clyde who retained control of the game, playing their usual brand of good passing football and had a number of good chances to clinch the three points against a disappointing Brechin side who have yet to win a game.
However, there was no further scoring and Clyde's draw at Glebe Park, after an eventful and tousy match, keeps the unbeaten run going and positions the Bully Wee just three points off the lead.
www.clydefc.co.uk
Brechin City and Clyde had to settle for a draw after a stormy encounter that saw both sides reduced to 10 men.
New home signing Gerry Britton great pass set up Stephen Hampshire for an early opening goal for Brechin.
Alex Williams shot wide from a great position for Clyde before Paul McHale's drive somehow found its way past goalkeeper Craig Nelson.
Both sides found themselves a man short after an hour, when Gerry Britton and Neil McGregor were sent off.
BBC Online