The only goal of the game came after just eight minutes when City skipper Dougie Hill diverted the ball into his own net following a Conner Duthie corner.
City hit back with their first real attack of the match six minutes later when good build-up play between Sean Burns and Dene Shields created an opportunity for Jordan Sinclair but his drive from just within the penalty-box was blocked by the home defence.
Stenny then had a chance to go 2-0 up after 21 minutes when Duthie made space for himself at the right edge of the penalty area and crossed across the face of the goal for Mark McGuigan but his header went narrowly over the bar.
In the 34th minute, Kalvin Orsi played a good pass forward to Burns who had sneaked in behind the home defence and he appeared to be impeded by Kieran Gibbons but referee Barry Cook took no action.
However, the Warriors midfielder had no such good fortune just seconds before half-time when he tripped City midfielder Jamie Henry with referee Cook producing a second yellow card which meant that the hosts were reduced to ten men.
The ten-men Warriors obviously had to change formation after the break and it was no surprise that the visitors with the extra-man advantage had the bulk of possession and pressure in the opening stages of the second-half and this pattern continued as the home side, understandably dug in a little deeper to protect their lead.
Former City keeper Graeme Smith was called into action in the 79th minute when he brought off an instinctive save from a Burns drive and the visitors came close again in the 83rd minute when a Shields close-range overhead kick went narrowly past the post and at the other end seconds later, City keeper Conor Brennan brought off a good save to thwart Duthie.
Dods’ side were keeping up the pressure in the closing stages and Smith came to his side’s rescue again with five minutes remaining when he brought off a good save to tip a Boris Melingui drive around the post.
Despite further late pressure from the visitors, the Warriors held on for a comfortable and deserved three points.
Stenhousemuir boss Brown Ferguson was pleased with two differing halves of football as his Stenny side dominated the first period before Kieran Gibbons seen red, forcing the hosts to dig in for the second period.
Ferguson spoke on his side’s first half performance, saying: “I thought we controlled it, and we were comfortable. We merited more than a 1-0 advantage going into half time.
“The performance was good and there was a good endeavour about us.
“I thought our control was good, with and without the ball, I would have maybe liked to have seen us create a few more chances but I was really pleased.”
Gibbons’ red card came right on the stroke of half time, changing Ferguson’s team talk completely - but his side followed their second half instructions to the letter, and ground out a 1-0 victory.
“We get the sending off coming into half time which changes our attitude in the second half.
“It was a very determied and brave performance. The players carried out the game plan very well and kept Brechin away from our goal.
“Our defence was excellent and Graeme made some outstanding saves when he had to.
“It was a different performance second half, one we spoke about at half-time and went out and implemented to perfection.”
Stenny’s next fixture is away to Raith Rovers on Saturday.