The Nigerian striker had been playing with a bandaged head, but discarded the protection before supplying the final header to an earlier one from sub Steve Brooker.
A free signing from Luton Town in the summer Showunmi has now scored eight times in a dozen starts.
Carlisle, who pride themselves on their low card count, picked up three in the first half which was prickled with ill-feeling.
But there seemed neither rhyme nor reason behind the first of them which saw Chris Lumsdon's third minute protests to referee Danny McDermot bringing out a yellow. But the anger in the game spread by a challenge from Carlisle's Kevin Gray on Showunmi.
It left the big striker needing touchline treatment for a cut head but he returned heavily bandaged after a five-minute absence.
He re-started with a quick burst down the central channel, a run abruptly ended when Peter Murphy brought him down with a sliding tackle from behind for card number two.
Gray's challenge had brought Bristol's manager Gary Johnson on to the pitch when a free-kick wasn't given and soon there was a skirmish on the other side of the field involving City's Phil Jevons and Carlisle's Kevin Harper.
The referee let both off with a lecture but the spat took time to work its way out of the game.
While it was departing Carlisle set up the better chances including a long-range shot from Karl Hawley which rattled the hoarding just behind Adriano Basso's left post.
Harper on the left and Kevin Gall on the right worried City with their speed and after Basso had saved well, City were indebted to Liam Fontaine for a tackle which lifted a shot from Harper over the bar.
Gall set that one up from inside the byline with a neat cross, but then he undermined a good half by collecting a booking for kicking the ball away at a free-kick.
City, who were being out-gunned in the middle of the park, found more determination in the second half and Jevons was released to go forward more.
The club's top scorer responded with a decent header from a Lee Johnson cross and then drew a sharp near-post save from Keiren Westwood as he powered in a 25-yard free-kick.
Both sides used their full complement of subs in a bid to open up their opponents and Brooker was the most significant of them with his header leading to the winning goal.