Midfielder Fraser Aird opened the scoring for the champions in the 22nd minute when he capitalised on a mistake by City full-back Jonny Brown before Brechin striker Robert Thomson equalised four minutes into the second half.
Midfielder Ian Black was carried off on a stretcher in the 65th minute after a challenge from defender Graham Hay and his replacement Clark, who scored the winner in the Gers' 4-3 win at the same venue last October after coming off the bench, headed the visitors back in front.
It was a workmanlike display by the Ibrox side and no more.
Ally McCoist's men have a Ramsdens Cup final against Raith at Easter Road in two weeks' time before a William Hill Scottish Cup semi-final against Dundee United at Ibrox and performance levels will have to increase if hopes of a treble are to be realised.
The most famous hedge in Scottish football partly encased part of the small ground where 3,070 fans watched the Brechin players applaud Rangers on to the pitch in tribute to the visitors' title win.
The home side had to change their plans in the 19th minute when Greg Cameron replaced the injured Paul McLean but the match turned within the space of a minute soon afterwards.
Referee Andrew Dallas controversially booked Alan Trouten for simulation in the 21st minute when the Brechin forward pounced on a poor pass from Gers defender Richard Foster before going to ground as he went past Ibrox keeper Cammy Bell.
It looked like a valid penalty claim on first viewing but certainly no dive and the home side complained bitterly.
However, they had more to moan about 60 seconds or so later when full-back Jonny Brown slipped in attempting to deal with a long Black pass, allowing Aird a clear run on goal and he confidently slipped the ball past former Gers keeper Graeme Smith.
Rangers midfielder Nicky Law was then replaced by Sebastien Faure after picking up an injury as the Ibrox men began to take control of the match.
Five minutes from the break, however, with Brechin finishing the half strongly, Bell dived to tip a long-distance drive from Darren Petrie over the bar for a corner which came to nothing.
It was not looking like Brechin's day as they were forced into another change before the interval when Ryan Ferguson came on for the injured Brown.
However, four minutes after the restart the home side were level.
Rangers failed to clear their lines properly under pressure and when Cameron's cross from the right came to the near post Robert Thomson steered it low past Bell.
It was the first goal the Ibrox side had lost on their travels since they conceded three in their victory at Brechin earlier in the season and it inspired City into believing they could end the Gers' unbeaten league run.
However, that enthusiasm was quashed almost as soon as Clark replaced Black, the former Queen of the South player moving in unmarked at the back post to head Jon Daly's cross past Smith from close range.
The goal eased the Ibrox nerves and Aird might have made it three, only to drag his angled-drive wide of the target with only Smith to beat, before skipper Lee McCulloch headed a Dean Shiels free-kick over the bar.
In the end Rangers ran out comfortable winners but injuries to Law and Black will put a dampener on the victory for McCoist as he looks to bigger games over the next few weeks.