The left wing-back marked his Robins debut with an 83rd-minute thunderbolt to cancel out Lukas Jutkiewicz's first of the season.
Blues took the lead after 64 minutes and seemed set to mark the first home match of Pep Clotet's tenure with a morale-boosting victory.
All of that came after a tight first half which produced just two shots on target, the first, for the hosts, came in the eighth minute.
That was delivered by new signing Fran Villalba, who joined from Valencia on a free transfer on Wednesday, when he drove in a shot from 25 yards.
Daniel Bentley tipped over the bar, giving Blues a corner from which they should have scored.
The Spaniard floated over a cross which the unmarked Gary Gardner headed down into the ground and on to the roof of the net.
Midway through the first period, Bristol City had their best opening when Kasey Palmer sent Benik Afobe free down the inside left.
Just inside the area, Afobe opened his body to curl a right-footed shot past Lee Camp but the Blues goalkeeper pushed the ball to safety.
Gardner came close in the 26th minute when he surged infield off the right touchline and lifted a shot slightly too high and wide from near the edge of the area.
Palmer did likewise four minutes before the break as the half ended goalless.
The second period was far less cagey with both teams engineering good opportunities before Jutkiewicz broke the deadlock.
The striker was frustrated when he saw his 57th minute drive parried up and narrowly wide by Bentley.
Adam Nagy then got a clear sight of Birmingham's goal on the hour, when he charged down Kristian Pedersen's clearance and drove the ball into the turf, which allowed Camp to beat away.
Four minutes later Jutkiewicz finally beat Bentley when he rose highest at the back post to power Marc Roberts' lofted cross into the back of the net.
The Robins responded brightly and, with a quarter of an hour remaining, Afobe was put clear again.
Leaving Roberts trailing in his wake, the loan striker tried to lift the ball over Camp only to see his effort blocked.
But the visitors eventually levelled with seven minutes remaining when Palmer picked out Rowe on the overlap and the former Doncaster man drove powerfully across Camp and inside the far post.