Luck again deserted Andy King as he took charge of Swindon for probably the last time as his directors look for someone else to coach the team.
A free kick in the 12th minute started their slide to a tenth defeat in 12 matches.
Bristol City captain Tommy Doherty latched on to the free kick in the centre circle, and hurried the ball on to Scott Murray who was breaking in fast from the right flank.
Murray chested it down before angling a confident shot out of the reach of keeper Bart Griemink.
It was his ninth goal of the season and with less than 12 minutes gone it was the blow beleaguered King feared.
Swindon's best chance of the game had come and gone in the second minute when Eric Sabin sent his header sailing high over the bar.
Swindon went on to see rather more of the ball in the first half but the accuracy of the final pass, so common to struggling sides, was just not there.
City, without ever reaching the fluency of their recent games, were in control.
Murray went close to another goal with a shot under the keeper's body but centre back Matt Heywood, who had an outstanding game, dived in to clear off the line.
City's second goal came in the 38th minute when the lively Christian Roberts played a ball inside to Brian Tinnion.
Swindon dropped off and Tinnion, seeing a gap, fired off a left-foot drive from 25 yards that flew in to the keeper's top right-hand corner.
City cruised through the second half to secure their fourth win in a row although they conceded too many thoughtless fouls.
However, the pace of Murray and Roberts always stretched the struggling Swindon defence.
After the game Swindon's skipper Andy Gurney said: "We all feel sorry for the stick the boss has been taking.
"He's a good bloke and a good manager and has the dressing room with him."