Loan star Darius Henderson scored twice to give Swindon victory in this West Country derby - just three days after joining The Robins.
He signed initially on a month's loan and his goals gave Swindon their first win in eight attempts against their rivals.
The white hot atmosphere of a derby had seen Henderson off to a yellow card start for a fifth minute clattering challenge on Christian Roberts.
But his awareness and height were soon posing problems for Bristol City's defence and midway through the first half he made the breakthrough.
After Steve Phillips pushed his angled shot away for a corner the swiftly delivered set piece was headed in by Henderson who out jumped his marker Matthew Hill.
It could of been a lot worse for City as Henderson hit both posts - one with a running shot and the other a header desperately touched on to the post by Phillips.
For a vital 10 minute period City completely lost the plot. Midfielders Roberts and Tom Doherty were booked and central defender Danny Coles could have followed when he brought down Sam Parkin.
When they pulled themselves together City hit back with a goal in added time by Doherty after Tinnion had turned the ball into the box and Lee Miller had jumped to distract keeper Rhys Evans.
Swindon came out for the second half determined to dominate play and went back in front on the hour mark.
Once again a set piece was the home side's undoing. This time a foul by Roberts saw a free-kick swung in from the left for Henderson to again out jump the defenders.
For the closing minutes Swindon were down to 10 men after losing defender David Duke for collecting two yellow cards but the visitors held on for the three points.