Tommy Mooney had Swindon's first real goal chance after 15 minutes when a Bristol City mistake in defence lead to Mooney finding the ball at his feet, but Mooney's hurried shot missed.
Miglioranzi also had a good chance to score for Swindon in the first half, but his shot went high into the crowed Stratton Bank.
The first half had seen few real chances by either side, until with one minute to go Matt Heywood's passback went to Bristol City's Peacock who was able to pass to the unmarked Roberts to score from close range.
Swindon came out in the second half looking more likely to score, with Parkin and Mooney both having chances.
Mid way through the second half King bought on Rory Fallon to replace Andy Nicholas.
Fallon then scored a goal of the season after 74 minutes with an overhead kick from 25 yards which beat the 'keeper and just dropped into the top of the goal.
Swindon had chances to win it, but it was Bristol City who missed the best chance to win when 2 minutes into stoppage time when the ball rolled across the line, but somehow the City players couldn't force the ball into the back of the net.
Overall a draw was a fair result with both sides having chances to win, The draw leaves Swindon still in 5th place needing a win against Luton on Mondday to help confirm their place in the play off's.