Coventry came close to scoring within a minute of kick off after an unforced error from Tottenham allowed Jack Rudoni a shot on goal, and although Fraser Forster comfortably turned it around for a corner, the mistake seemingly set the tone for the visitors' first half.
Spurs went on to dominate the possession, holding 74% of the ball in the first 45 minutes, but they failed to register a single shot on Coventry's goal as their attacks consistently broke down due to a lack of quality in the final third.
The hosts, on the other hand, were clearly emboldened by their early opportunity and threatened to break the deadlock with several well-executed counterattacks; ultimately, though, the score remained level going into the break.
It was more of the same from Spurs after the restart, narrowly staying level thanks to Ben Davies's heroic goal-line clearance after yet another defensive error, but just minutes later Coventry finally had the goal they more than deserved as Brandon Thomas-Asante converted from a cross into the middle of the area.
The Sky Blues had several glorious chances to add a second goal and surely secure their progression into the next round, but Tottenham managed to stay within reach and give themselves a fighting chance as the final whistle approached.
Coventry did live to regret their missed opportunities as Tottenham finally put together multiple quality pieces of attacking play in the final minutes, levelling through Djed Spence in the 88th before Brennan Johnson scored a chipped winner in the 92nd minute to give Spurs a comeback victory.
COVENTRY CITY VS. TOTTENHAM HOTSPUR HIGHLIGHTS
Ben Davies goal-line clearance vs. Coventry City (56th min, Coventry City 0-0 Tottenham Hotspur)
A long ball was played forward by Ben Wilson, unbelievably sailing over the Tottenham defence and allowing Norman Bassette to race towards goal.
Bassette was able to head the ball past the onrushing Forster, but the striker went down under the fair challenge of Radu Dragusin, leaving Haji Wright a chance to shoot at an empty net.
The strike looked destined for goal but a heroic goal-line clearance from Davies prevented Coventry from taking the lead and kept Spurs level.
Brandon Thomas-Asante goal vs. Tottenham Hotspur (63rd min, Coventry City 1-0 Tottenham Hotspur)
A positive piece of football sees Coventry play their way out from the back, with Rudoni being fed the ball before making a charge towards Tottenham's half.
The attacking midfielder laid the ball wide left to Bassette, who delivered an inch-perfect first-time cross into the area, allowing Thomas-Asante to slot into the near corner to give the hosts the lead.
Djed Spence goal vs. Coventry City (88th min, Coventry City 1-1 Tottenham Hotspur)
Tottenham finally put together a quality piece of attacking play as James Maddison flicks the ball around the corner for Dejan Kulusevski, who feeds an inviting pass into the path of Spence.
The defender beats his marker to the ball and is able to toe-poke his effort past the keeper, equalising for Spurs in the final minutes.
Brennan Johnson goal vs. Coventry City (92nd min, Coventry City 1-2 Tottenham Hotspur)
A turnover in the middle of the park gives Rodrigo Bentancur possession, and the midfielder quickly looks up before playing a beautiful pass through to Johnson.
The winger does not even need a touch as he lifts the ball over Wilson and into the far corner, topping off a dramatic evening for Tottenham.
MAN OF THE MATCH - BRENNAN JOHNSON
Johnson spared Postecoglou and Tottenham embarrassment with his fine chipped finish in the 92nd minute to secure a late comeback victory against Coventry, a moment more than worthy of the man of the match.
The winger, who came on in the 18th minute, was a rare threat for Spurs with several promising moments throughout the match, successfully making one dribble and attempting four crosses in his attempts to drive Tottenham up the pitch before eventually scoring the decisive goal.
COVENTRY CITY VS. TOTTENHAM HOTSPUR MATCH STATS
Possession: Coventry City 30%-70% Tottenham Hotspur
Shots: Coventry City 15-9 Tottenham Hotspur
Shots on target: Coventry City 5-4 Tottenham Hotspur
Corners: Coventry City 7-7 Tottenham Hotspur
Fouls: Coventry City 9-10 Tottenham Hotspur
BEST STATS
WHAT NEXT?
Coventry City are now without a victory in three matches across all competitions, something Mark Robins will look to address when his side host Swansea City at The Coventry Building Society Arena in the Championship on Saturday.
Tottenham will have to wait just under a week until they find out who their fourth-round opponents will be, with the draw not taking place until the third round wraps up on September 25, leaving Spurs to focus on a Premier League game against Brentford on Saturday in the meantime.