Jan Vertonghen propelled Tottenham into the top four of the Premier League with a second-half strike that finally broke stubborn Swansea.
The Belgium defender showed composure on 75 minutes to sweep a free-kick from Kyle Walker past Gerhard Tremmel.
It was the reward Tottenham deserved after controlling a disappointing encounter at White Hart Lane that failed to match expectations before exploding into acrimony deep into injury time.
Swansea striker Michu was caught by Hugo Lloris as the goalkeeper punched the ball clear and fell heavily to the floor.
While those players closest to the stricken Michu furiously waved to the touchline for medical assistance, Spurs played on through substitute Andros Townsend.
Incensed by Townsend's perceived lack of sportsmanship, defender Chico Flores confronted the forward and several Spurs players and was only placated when his Spanish compatriot Michu climbed to his feet.
Sorely missing the penetration of the injured Gareth Bale, Spurs struggled to break down opposition that defended stoutly without offering much threat themselves.
Andre Villas-Boas could be heartened by his side's third clean sheet of the season and the energy of the irrepressible Jermain Defoe, but playmakers Clint Dempsey and Mousa Dembele offered little.
Emmanuel Adebayor limped off with a second-half injury and there was a brief injury-time cameo from Scott Parker, making his first appearance since suffering an Achilles injury at Euro 2012.
Spearheaded by the Premier League's top scorer Michu, Swansea rarely troubled the home goal and looked lethargic after their midweek Capital One Cup quarter-final victory over Middlesbrough.
Michael Laudrup brought in Ashley Williams and Ki Sung-Yueng to freshen up a team that was continuing to thrive in the top flight.
The pattern was much the same for both halves, Swansea enjoying a bright start before Spurs took control in pursuit of the goal needed to rescue a largely drab spectacle.
A decisive tackle from Williams stopped Defoe in his tracks on the edge of the area after the Swans had opened the first half strongly, but moments later the lively England striker forced a save from Tremmel.
Swansea's defence was then split open twice more, first by Dembele's steal from the dawdling Michu and then by another slick move that saw Flores stick out a leg to block Adebayor.
Defoe was a constant menace with one turn and shot ghosting the right post as Swansea continued to be picked apart by their opponents' slick passing.
Aaron Lennon butchered one fine chance, producing a poor final ball when he should have taken the shot himself after dashing free down the right.
White Hart Lane was reduced to virtual silence as the match entered a lull, Spurs unable to score and Swansea rarely leaving their own half.
William Gallas showed speed and timing to close down Michu, and at the other end a powerful 40-yard drive from Walker cannoned into the chest of Tremmel, who would have been beaten had the attempt been better placed.
An audacious lob by Michu from just inside Spurs' area clipped the roof of the net as a relieved Hugo Lloris back-pedalled to cover.
Wayne Routledge darted around Gallas early in the second half and found Nathan Dyer but his glancing header failed to hit the target.
The fingertips of Tremmel frustrated Adebayor before Walker skied a shot into the stands, wasting the chance after a dynamic interchange between Defoe and Lennon.
Villas-Boas replaced the ineffective Dempsey with Gylfi Sigurdsson as a poor match wore on and then Adebayor limped off with Townsend coming on.
The goal that Spurs had been threatening for most of the game arrived in the 75th minute, a Swansea head nudging the ball into the path of an unmarked Vertonghen who made no mistake with a low shot into the right corner.
The visitors pressed throughout the five minutes of injury time, before Michu was felled and the game ended with Flores remonstrating against anyone in a white shirt.