Spence and Johnson rescue Tottenham in last minute to beat Coventry in Carabao Cup | Carabao Cup

Substitutes Brennan Johnson and Djed Spence scored in the final two minutes of this thrilling Carabao Cup match, allowing Tottenham Hotspur to recover from Brandon Thomas-Asante's deserved goal and sneak past Coventry City into the fourth round. At least that's a route to a trophy rescue for Ange Postecoglou.

Penalties were the end of Mark Robins' side when they lost the Championship play-off final to Luton Town 16 months ago and the FA Cup semi-final to Manchester United last season. And it looked like they were in for another 12-yard effort until Spence, cleverly set up by Dejan Kulusevski, slotted home from close range.

But until James Maddison, Son Heung-Min and Kulusevski came on, Spurs were largely outmatched – and outgunned – by the spirited Championship side. Then, in injury time, Rodrigo Bentancur Johnson played in goal and the Welsh winger, who was so abused online after his performances in Sunday's north London derby that he deleted his Instagram account, scored the winning goal.

While both teams had mediocre starts to their respective league seasons, the pressure was clearly on Spurs. Few neutral observers can object to a manager who shows ambition and shoots from the hip, and Postecoglou won many hearts of impartial observers with his belief that he “always wins something in year two”.

He may have done that in Australia, Japan and Scotland, where he won the title in his second season as manager, but the Premier League is a different calibre altogether. All of this suggests he would need to win a trophy, something Spurs have not done since 2008, to continue his second season winning streak, and the Carabao Cup is an easier target than the FA Cup or Europa League.

So it seemed a bit of a risk for Postecoglou to make eight changes to the team that lost 1-0 to Arsenal on Sunday. Coventry also made seven changes after all their heroics of the last 18 months, but Robins' team looked far more prepared for this cup, at least in the first half.

It is 11 years since these teams last met and Spurs have never been to this stadium before, but Coventry were in no mood to be overly hospitable. This was their third game in the competition, following 1-0 wins over Bristol City and Oxford United, and they sensed unease in the Spurs ranks from kick-off. When Fraser Forster, making his first start for Spurs, played the ball to Lucas Bergvall, Jack Rudoni was quick to capitalise on the loose contact. The former England goalkeeper had to parry the powerful cross-shot with 45 seconds left and a corner was awarded.

The omens did not improve for the visiting side, who made extensive changes to their first challenge in this competition 12 months ago, losing on penalties to Fulham when Wilson Odobert went out injured and had to be replaced by Brennan Johnson.

On this side, where Archie Gray made his first competitive appearance for Spurs since his £30 million move from Leeds, Coventry twice came even closer to taking the lead just before half-time.

Left-back Jake Bidwell's excellent cross caused Spurs problems and from a clever cross Rudoni was too late to fire a half-volley which Forster parried with his legs. Moments later Norman Bassette broke through on the left and fired a superb shot which Forster tipped over the bar. However, referee Darren England did not acknowledge it and awarded a goal kick.

While Coventry could be pleased with their first-half performance, Spurs were booed for it. Postecoglou replaced Destiny Udogie with the less-regarded Spence and Johnson's shot deflected, but it was still Coventry who kept pushing.

Again it was that half-left channel that Coventry probed. One of Thomas-Asante's shots was blocked, then the ever-dangerous Belgian teenager Bassette forced Forster into a save.

The sizeable home crowd sensed another upset was in store. Their greatest cup experiences against Premier League opponents last season were against Wolves at Molineux and Manchester United at Wembley, but this time the metaphorical lid came off the CBS Arena when Bassette crossed straight after James Maddison and Son Heung-Min had come on and Thomas-Asante calmly inside-footed home.

Both teams strengthened themselves with substitutions but Coventry were still closest to scoring another goal until the late double strike. Ellis Simms, who had scored six goals in this FA Cup run, came on and headed a Bidwell cross just wide before firing a low shot that Ephron Mason-Clark almost skidded into the net.