Their performance at Turf Moor was far from convincing, however, and they will need to improve against an out-of-form Manchester United on Saturday, a game which feels seismic for Nuno Espirito Santo and Ole Gunnar Solskjaer.
Reeling from the humiliating 5-0 defeat to Liverpool, United’s confidence will be at rock-bottom and Nuno's side should aim to put a leaky defence under pressure from the off.
But there has been little in recent weeks to suggest that Spurs currently have what it takes to put any opponent to the sword, let alone a team with United’s individual quality.
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Wednesday's contest was another affair low on quality, with neither side managing a shot on target in the first half.
Spurs improved after the interval, although it was obviously a low bar, and Lucas Moura’s well-taken header settled the tie before the visitors withstood a late Burnley rally.
While Solskjaer’s side are there for the taking on Saturday, they are also certain to offer a reaction to the Liverpool defeat, making them dangerous opponents for Spurs if they are as flat as they were for long periods in Lancashire.
That said, they were deserved winners on the balance of play and if Harry Kane or Giovani Lo Celso had been more clinical, the scoreline might have been far more comfortable.
Kane misfires again
It was another frustrating outing for Kane, who twice miscued left-footed shots in Tottenham’s best openings of the first-half.
Kane was put through by Lo Celso in the first few minutes but fired well wide from 18 yards, before shanking a difficult volley high over the bar.
They were ultimately Kane’s headline involvements but he nonetheless played his part in Spurs’ win, including with a pass in the build-up to the goal, and was unlucky not to finish the game with an assist after playing in Lo Celso in the second-half.
Clearly, Kane is remains some way from his ruthless and explosive best but there have also been signs in the last few matches that he is very gradually getting there.
He impressed against Newcastle and might have finished Sunday’s defeat to West Ham with a goal and assist. The same was true here.
The England captain still looks a shadow of his best self but Spurs and Nuno can take encouragement from the fact that he is, at least, going in the right direction.
Spurs’ back four holds firm
Nuno must have been pleased with a solid defensive display, with back-up goalkeeper Pierluigi Gollini having just one – comfortable – save to make.
Emerson Royal remains a work in progress but was solid and finished with an assist after his deflected cross was met by Lucas' firm header into the ground and past Nick Pope.
Cristian Romero and Davinson Sanchez were also committed at centre-half, the Argentine snapping into tackles and blocks while Sanchez mopped up long balls over the top.
The Colombian made a crucial late intervention as Burnley enjoyed a spell of pressure and, as poor as the Clarets were, Spurs deserve credit for keeping them at arm’s length.
A worry for Nuno was a first half injury to Bryan Gil, who was replaced by Lucas after 25 minutes after going down on the touchline.
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