Goals from Peter Lovenkrands and Jonathan Spector were cancelled out by Cody McDonald and Kevin Kilbane in normal time, before Carl Baker notched the winner in extra-time.
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Lee Clark made three changes to his side following the weekend fixture with Watford as Lovenkrands, Colin Doyle, and Morgaro Gomis returned to the starting line-up.
Jack Butland, Nikola Zigic and Nathan Redmond were the trio that made way, with the latter two named on the substitute’s bench.
The hosts made two changes as league debutant William Edjenguele and Jordan Willis return at the expense of Richard Wood and Kevin Malaga.
Blues had left themselves too much to do in recent weeks following slow starts, but they could not have started this tie in a more positive fashion. Lee Clark was testing out a new diamond formation, with Chris Burke at the attacking pivot and Hayden Mullins anchoring and it came to fruition immediately.
Just four minutes were on the clock when Burke won a free-kick in behind the midfield. Darren Ambrose delivered an inviting ball into the box and Lovenkrands was all alone in the middle to nod home an early opening goal.
Set-pieces were evidently causing the Sky Blues problems and Clark’s men could have had a second just two minutes later when Curtis Davies rose highest from another Ambrose delivery, but the centre-back could only manage to connect with his heel and the ball was cleared.
Stephen Elliott swept over a half-chance from 12 yards as Coventry tried to draw level in the tenth minute, but they almost found themselves with a bigger deficit just three minutes later.
Burke won the ball in the centre-circle and proceeded to drive forward, relishing his new-found freedom and laying the ball off to Gomis, who slipped an inch-perfect ball in behind the full-back Willis for King to pull back to the penalty spot where Burke had continued his run. However, the Scots side-footed effort struck the underside of the crossbar and bounced clear.
However, in the 19thminute, Blues were dealt a sucker punch as Kilbane slipped a ball in behind the Blues defence for McDonald who slid the ball beyond a helpless Doyle and into the bottom corner against the run of play.
It got worse for Blues three minutes later when Adam Barton and Baker linked-up down the right-hand side and the latter’s cross broke at the back-post for the veteran Kilbane who lashed home a left-footed strike.
Both sides had chances to score again as the first-half drew to a close. Barton fired wide from distance for the hosts and Marlon King had a deflected strike from distance well held by Joe Murphy before Baker’s mazy run and shot was cleared off the line by Jonathan Spector.
There were encouraging signs for Clark, though, as good link-up play between Spector and Lovenkrands on the edge of the Coventry box lead to Ambrose having a shot deflected over.
That previous good play was on show again in the 44thminute as Blues deservedly drew level. Spector again brought the ball out of defence and exchanged passes with Gomis, King stepped over the return pass and Spector took one touch before firing his first goal for the club past Murphy to send the teams in level at the break.
The second period started without the attacking verve of the first and it took until the 57thminute before either shot had an attack of any real note. Burke was the man who led the counter-attack from just inside his own half and managed to stride forward unopposed until he reached the edge of the home box, he then slipped a ball down the left-hand side of the area which Gomis latched onto, but fired his effort wide.
Blues made two substitutions in a five-minute period as Redmond replaced Ben Gordon in the 66thminute, with Spector moving to left-back and Mullins to right-back. The backline was altered again four minutes later as Davies left the field hobbling after a late tackle by McDonald and was replaced Pablo Ibanez.
In the 72ndminute, Redmond almost repaid Clark’s faith as he cut inside from his right-wing station and fired a left-footed effort along the floor from 25 yards, but Murphy got his whole body behind the ball.
The young winger was looking lively and minutes later he escaped down the wing, but his cross was cleared by Reece Brown with King lurking behind him.
Clark made his last substitution with 11 minutes remaining as he brought Adam Rooney on for his first piece of competitive action of the season, replacing Lovenkrands.
Blues were pressing for a winner in normal time and, again, Redmond was looking lively. This time, after receiving the ball on the edge of the area he slalomed away from two Coventry defenders before attempting to curl an effort in to the far corner that was read by Murphy.
Redmond was again causing problems and the youngster drove in to the box but saw his cross blocked behind for a corner by Chris Hussey. The local lad took the resulting set-piece and at the back post Ibanez nodded wide from a tight angle as the second-half finished with the teams level.
The visitors looked the more likely winners as extra-time began and it took them just three minutes to work their first opening. Redmond drifted in from his flank and drilled a pass to the feet of King. He laid the ball back to the winger and his left-footed effort was blocked.
A creative corner between Burke and Ambrose found the former Crystal Palace man on the edge of the area, but as the ball sat up, he fired over with a left-foot strike.
However, seven minutes into extra-time, Coventry scored what turned out to be the winning goal. A deep cross from Hussey evaded Caldwell, but Baker’s first-touch rebounded back off the Blues captain. Then, Gomis and Spector got in each other’s way as they tried to clear and Baker stole in to steer the loose ball past Doyle.
Blues tried to strike back as Gomis’ 25-yard shot clipped the top of the crossbar, but Clark’s men went in behind at the interval.
The manager tweaked the system in the break and the visitors came back out sporting a 3-4-1-2 formation as they pushed to find an equaliser.
They almost had the leveller in the 110thminute when Spector nearly notched his second of the night, rising highest to meet Burke’s corner, but the American nodded over whilst under considerable pressure.
The hosts were attempting to run the clock down and were being limited to shots from distance as Ball fired harmlessly wide with a rash effort.
Blues had a late penalty appeal turned down as Ambrose’s overhead kick was blocked, but Clark’s side could not find an equaliser as the hosts progressed to the third round of the Capital One Cup.
Coventry City: Joe Murphy; Chris Hussey, Carl Baker, Cody McDonald (Callum Ball, 90), Steven Jennings, Stephen Elliot, Kevin Kilbane (c), Adam Barton (Gary McSheffrey, 80), William Edjenguele, Jordan Willis (Cyrus Christie, 65), Reece Brown.
Subs (Not Used): Chris Dunn, Kevin Malaga, Roy O’Donovan, Billy Daniels
Goals: McDonald (19), Kilbane (22), Baker (97)
Bookings:Edjenguele (25), McDonald (61)
Blues: Colin Doyle; Jonathan Spector, Curtis Davies (Pablo Ibanez, 71) Steven Caldwell (c), Ben Gordon (Nathan Redmond, 66); Chris Burke, Hayden Mullins, Morgaro Gomis, Darren Ambrose; Marlon King, Peter Lovenkrands (Adam Rooney, 79)
Subs (Not Used): David Lucas, Ravel Morrison, Wade Elliott, Nikola Zigic
Goals: Lovenkrands (4), Spector (44)
Bookings:Mullins (67), Gomis (107)
Attendance:10,859 (3,859 away)