Marlon Pack fired the Robins in front after 12 minutes with a sweetly-struck right-footed free-kick from 25 yards following a foul by Michael Morrison on Reid.
It was 2-0 in the 27th minute as Famara Diedhiou nodded down a Joe Bryan cross into the path of Reid and he hammered home a low drive on the half-volley from 10 yards.
Lukas Jutkiewicz put Birmingham back in the game seven minutes later, making room on the right side of the box to beat Frank Fielding at his near post with a low left-footed shot.
But Bristol City substitute Matty Taylor settled the outcome with six minutes remaining, sliding to convert Reid's low cross from the right to give his team only their fourth win since Boxing Day.
A thrilling first half saw Birmingham create the first chance when Jutkiewicz glanced a header wide from Wes Harding's fifth-minute cross.
The visitors might have been ahead at the break had it not been for squandered opportunities. Jeremie Boga failed to beat Fielding one-on-one in the 17th minute, the Bristol City goalkeeper spreading himself to save.
Moments later Fielding could only palm out a low Jutkiewicz shot from an angle and Jacques Maghoma put the rebound wide from close range.
Milan Djuric volleyed wide for the home side before Reid doubled their lead. But Blues went close again when Jota shot wide having been set-up by Maghoma's low cross.
Jutkiewicz deserved his goal and had another effort saved as the half-time whistle brought some respite for players and supporters alike. The atmosphere had been electric from the start, with 1,475 travelling fans playing their part.
Birmingham's Harlee Dean was booked after 55 minutes for pushing Diedhiou and from the resulting free-kick 30 yards out, Pack drove narrowly wide.
Bristol City almost increased their lead in the 62nd minute when their opponents allowed a Lloyd Kelly long throw from the left to bounce inside their box and Reid headed against the crossbar.
At the other end, Jutkiewicz headed wide from a Boga cross when he should have hit the target.
Birmingham then sent on Beryly Lubala for Boga and shortly afterwards the substitute was testing Fielding with a deflected shot which was parried for a corner.
Bristol City sent on winger Callum O'Dowda and Taylor, both back after long injury lay-offs, taking off their two big front-men Diedhiou and Djuric.
There were still chances at both ends as Bryan fired just wide for the hosts before Taylor's goal finally took the stuffing out of a battling Birmingham side.
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