Substitute Mark Harris added a second on the counter-attack on 87 minutes as the visitors pushed for an equaliser in a contest of few clear-cut chances.

Coventry came closest to scoring when Alex Smithies saved brilliantly from Viktor Gyokeres' header.

Cardiff have turned their home league form around, having lost nine of 10 matches in front of their own fans before this hat-trick of victories.

They rise to 19th, while Coventry remain 12th, with their faint play-off hopes diminished further.

Cardiff manager Steve Morison made four changes to the side beaten at his old club Millwall on Saturday with Will Vaulks, Isaak Davies and Max Watters recalled, while academy product Eli King was given a first league start for the Bluebirds.

Coventry boss Mark Robins made three changes to the side that came from behind to beat Reading with Jamie Allen, Jordan Shipley and Kyle McFadzean recalled.

It was the hosts who fashioned the first opportunity, with Watters heading at goalkeeper Simon Moore from Bagan's cross, but Moore did well to prevent his momentum from carrying the ball over the line.

However, the visitors soon grew into the contest and Shipley and Callum O'Hare shot wide before both Aden Flint and Alex Smithies challenged O'Hare in the penalty area within seconds, but referee John Busby rejected the Sky Blues' penalty appeals on both occasions.

Cardiff tested Moore again on 34 minutes when Watters fired a shot after Vaulks' ball over the top, with Moore knowing little about his save as the ball struck him on his head and deflected wide.

Curiously that was Watters' last key involvement, with the forward replaced on 37 minutes by Jordan Hugill.

Watters looked perplexed at being taken off and his disappointment was evident as he spent the duration of half-time sitting on the Bluebirds' bench.

It was Watters' replacement, Hugill, who could have put Cardiff ahead of 57 minutes, but he shot straight at Moore after Cody Drameh's run and cross carved Coventry apart.

It was the wing-backs who were the hosts' main attacking outlet and it was Bagan who finally unlocked Coventry's defence as he cut inside Ben Sheaf and curled an unstoppable right-footed effort past Moore.

Bagan scored his first Cardiff goal at Millwall on Saturday and made it two in two with a goal he will do well to top, aesthetically, in the remainder of his career.

The goal was a little harsh on Coventry and they responded well as O'Hare's cross was perfect for Gyokeres, but Smithies instinctively saved his diving header with an outstretched leg.

That proved vital as Cardiff wrapped things up on 87 minutes when Hugill found Harris, who cut inside and fired across Moore into the bottom corner of the net.

Cardiff City boss Steve Morison told BBC Sport Wales:

"It was a very good job well done from everyone, the staff, the players, every single one of them.

"We've shown tonight we have a good group of players and if we carry out our jobs, we will win games.

"First 20 minutes they were the better side, but they are a good team, they've been better and more consistent than us recently.

"We won 2-0, we got a clean sheet and ultimately that's what matters, but I hope our fans can see what is going on."

Coventry City boss Mark Robins said:

"I think the first one cost him [Callum O'Hare] a penalty, the first one looks like a dive as he's trying to get out of the way, the second one he has clipped him, so it could have been a penalty.

"We were below par in energy levels. This has been postponed because of Covid and us at full-tilt would have been a different story.

"There wasn't a great deal in the game but in the second half we knew we were below par with our energy.

"We didn't do enough, but we didn't have it in our legs to do it. No qualms with the result, it's where we are at the moment."