Guido Burgstaller, a summer signing from Rapid Vienna, struck early on in a relatively straightforward opening 45 minutes for Cardiff as Kim Bo-Kyung and Declan John both threatened to put things out of their hosts’ reach before the break.
Cardiff were made to wait until the 81st minute for a second as Mats Moller Daehli saw his left-wing cross turned in by Coventry defender Ryan Haynes. A quick response soon came through Shaun Miller’s volley, but the South Wales side held on to secure their progression.
Talk ahead of the tie was dominated by the future of Sky Blues boss Steven Pressley, but he played down speculation of a departure to Huddersfield after becoming odds-on favourite to replace Mark Robins.
Pressley brought Burge, Jack Finch, Billy Daniels and John Fleck into his side following their opening day 3-2 defeat away to Bradford City.
Ole Gunnar Solskjaer made wholesale changes from Cardiff’s 1-1 draw at Blackburn, with just Matthew Connolly, Aron Gunnarsson and Nicky Maynard surviving from the Ewood Park clash.
Gunnarsson was handed the captain’s armband against his former side, while there was a Cardiff debut for 18-year-old full-back Jazzi Barnum-Bobb.
Solskjaer’s men started brightly and it took them just under four minutes to get off the mark as Burgstaller hit his first goal for the club on his full debut with a low drive into the bottom corner.
His strike partner Maynard was the provider, teeing up the Austrian forward with a smart backheel after bringing down a long ball on his chest.
The pair showed signs of an understanding in attack during the early stages and soon linked up again as Cardiff threatened to double their lead almost immediately after going in front. This time it was Burgstaller creating the chance, but Maynard was unable to divert his cross on target.
The Championship side continued to dominate as Walls saw a low effort deflected wide from range before Kim came close with two chances in quick succession.
Burge’s Coventry goal was under siege but it was not until John burst into the area and let fly that he was truly tested with a smart save.
Attentions turned to the stands on the 35th minute as both sets of fans united in protest to hold aloft cards bearing the message ‘Let Down’.
Coventry have been forced to play in at Northampton’s Sixfields stadium since last summer and the 35th minute was a reference to the mileage from their original Ricoh Arena home.
The second half started in a similar vein with Cardiff pressing for a second and the lively Kim was in the thick of it once again as Burge pushed his curling effort away before equalling another long-range strike from Walls.
Josh McQuoid looked the most likely to make something happen for the hosts and he saw a looping header just evade the post before firing wide from inside the area.
Their best move came just after the hour as Danny Swanson burst away from his marker down the right and floated an inviting cross towards the back post. Jordan Clarke was arriving to meet it but could only plant his header into the stand behind Simon Moore’s goal.
Maynard threatened twice for the visitors, but Coventry continued to push for an equaliser as a mazy run from Swanson culminated in him dragging a strike wide before second-half substitute Shaun Miller blasted well over the bar after being fed through on goal.
The Sky Blues were soon made to rue their missed chances as Daehli, who replaced Burgstaller, broke down the left and Haynes poked the cross into his own net under pressure from Kadeem Harris at the back post.
Haynes quickly made amends at the right end, though, as his pin-point delivery was met by Miller to volley beyond Moore and ensure a nervy finale.
Coventry captain Andy Webster headed a corner agonisingly wide in stoppage time but the visitors managed to hold on and reach the second round.