Spurs manager Mauricio Pochettino said it was important to follow up their dramatic qualification for the Champions League last 16 in midweek with victory against Burnley in the league.
The Londoners needed Lucas Moura's 85th-minute equaliser at Barcelona on Tuesday to earn a spot in the knockout round, and another late strike on Saturday meant they keep up the pressure on the Premier League's top two.
This time it was substitute Christian Eriksen who came to their rescue when he slammed his shot past Joe Hart in the 91st minute.
"It is a very good week for us and a fantastic win for us today," Pochettino told BBC's Match of the Day. "It is so important to be focused and try to keep our energy.
"After the Barcelona game and qualifying for the next stage of the Champions League, it is difficult to find the way to perform like this.
"Today I congratulate my players' effort and the fans. It was a late victory but so important for us."
It looked as if the Clarets would come away with a deserved point following a tremendous defensive display. They limited Spurs to a handful of clear-cut chances, with Lucas Moura and Son Heung-min both going close, while Hart produced a magnificent save to deny Erik Lamela.
The victory moves third-placed Spurs to 39 points and within three of Liverpool in second. Burnley remain in 17th with 12 points - two points above the relegation zone.
Perseverance paid off for Tottenham in midweek and it did so again against Burnley.
Mauricio Pochettino's men tried several combinations to unlock the visiting defence, but time and time again they were thwarted. Most of their forays broke down on the edge of the area.
They did, though, break through on a handful of occasions, with Moura and substitute Son going close. The Brazilian, the hero against the Catalans last Tuesday, poked a volley wide before Son's angled drive just missed Hart's far post.
In between those two chances, Hart pulled off a superb stop to deny Lamela.
With seconds remaining Pochettino, wearing a woolly hat in wet Wembley conditions, looked a beaten man until one of his generals raised his spirits and brought the home support to their feet.
It was striker Harry Kane the provider, as he laid the ball into the path of Eriksen, who fired his shot beyond the reach of Hart.
The result was cruel on Burnley.
This was the sort of resolute performance against one of the 'Big Six' we got used to seeing from Sean Dyche's side last season. They defended from the front and restricted the space for attacking players Kane, Dele Alli and Lamela by hunting them down in pairs.
This focus on defence meant Tottenham keeper Hugo Lloris had a quiet time at the other end. The Frenchman did, however, suffer one of his lapses in concentration when his poor pass out of defence was almost punished by a header from Ashley Barnes.
Barnes also had a scissor-kick inside the area blocked by Kane in the first half.
Burnley manager Sean Dyche on BBC's Match of the Day: "Obviously we are frustrated and disappointed in the outcome but a lot of positives. My only gripe is we get done by a whack down the pitch.
"Inevitably we didn't deal with that final moment and they nick a goal. There were good signs from the mentality we know we have to win games. There is a resilience and organisation but we are playing a top side - it is difficult to come down here.
"Away from home against sides like this you have got to try and model a team that can still get a result. I feel for the players because they put a proper shift in today and did the basics well. The last three or four games we are getting back to what we can be - we need more attacking prowess but it is difficult."
