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Tottenham needed two late goals from Djed Spence and Brennan Johnson to beat second division Coventry 2-1 and avoid a surprise League Cup exit on Wednesday.
Spurs were heading for their third consecutive defeat when Brandon Thomas-Asante fired the Championship side into the lead after 63 minutes.
Tottenham head coach Ange Postecoglou responded to criticism following the 1-0 defeat to Arsenal in the north London derby on Sunday, stressing that he would continue his record of winning titles in his second season at multiple clubs.
However, the former Australian coach faced fierce reactions from his own supporters, who booed the decision to substitute Swedish youngster Lucas Bergvall early in the second half.
Coventry almost surprised Manchester United in the FA Cup semi-finals last season and had a glimpse of the upset when Norman Bassette delivered a superb cross that Thomas-Asante was able to score.
Postecoglou was on the verge of his second consecutive early exit in the competition, but he was spared embarrassment when Dejan Kulusevski linked up with Spence, who scored his first goal for Spurs in the 87th minute.
Tottenham sensed their chance and played Johnson in the second minute of injury time, who scored the winning goal.
With a 3-2 win against Wolves, Brighton also secured their place in the round of 16.
Carlos Baleba, Simon Adingra and Ferdi Kadioglu were goalscorers for the Seagulls.
kca/dj
