The Robins, possessing the worst home record in the Championship, were second best in the opening 45 minutes and went behind to Clive Platt’s cool finish.
Marvin Elliott headed level just before the break, much to the anger of the visitors who had centre-back Ben Turner on the floor nursing a blood wound to his mouth.
But the Sky Blues regained their advantage on the stroke of half-time, ironically courtesy of Turner’s second goal in as many games from close range.
The hosts improved after the break as they went in search of an equaliser but, despite hitting the crossbar through Elliott’s header, it was Coventry who were left celebrating their first win in four and first on the road since March.
Robins manager Keith Millen promised to look at both his side’s personnel and shape after seeing them go down 2-0 at home to Watford on Tuesday. And he did just that, making four changes and switching to a 4-3-3 formation.
Opposite number Aidy Boothroyd, again without Marlon King with City having failed once more to wrap up his potential signing in time, brought in Martin Cranie and Carl Baker from the side which lost 2-1 at Swansea in midweek.
And the Sky Blues boss will have been pleased with Coventry’s bright start having seen his charges firmly on the back foot in the first half of both their previous games against the Swans and Leicester.
And he was even happier when his side took the lead with their first real chance after 22 minutes.
Sammy Clingan floated an inch-perfect ball over the top to find Platt, who beat the offside trap and – one-on-one with David James – produced an assured finish low past the former England international.
The goal woke up the hosts somewhat, but Coventry continued to be more threatening in the final third and looked to be heading into the interval with a 1-0 lead.
That was until the 42nd minute when, with Turner grounded, Jonathan Stead burst down the right and crossed to the far post where Elliott was on hand to head home an equaliser.
Coventry’s protests fell on deaf ears but within three minutes they had regained their half-time lead when Turner nodded home defensive partner Richard Wood’s goalbound header from Clingan’s free-kick.
Keiren Westwood, widely regarded as the best keeper outside the top flight, underlined his credentials at the start of the second half with a diving save to tip Elliott’s header around a post.
The hosts were a different proposition after the restart and Elliott saw another header bounce off the turf and onto Westwood’s crossbar.
Bristol City continued to dictate the second half, but failed to create any further clear-cut chances against a Coventry side who also posed much less of a threat.
Nevertheless, it was they who held on for all three points and their first victory over their West Country opponents on any ground since 1979.