However, West Bromwich Albion missed a chance to move into the Champions League positions by drawing 0-0 at home to West Ham, extending the team's winless run to four games after its surprisingly strong start to the season.
Vertonghen, the Belgium captain, settled a tight match at White Hart Lane by meeting Kyle Walker's right-wing free kick with a low half-volley from just inside the area.
Tottenham is now level on points with third-place Chelsea, which has a game in hand. West Brom stayed sixth but the standings are congested below the top two Manchester clubs, with seven points separating third from 12th.
"For us, it's important to break out from the pack and join the top two," Spurs manager Andre Villas-Boas said.
"Until we find the stability in our run of results and distance ourselves from the pack, things can change dramatically."
The Tottenham-Swansea match ended in controversy, however, with members of both benches spilling onto the pitch after visiting striker Michu was left prone on the ground after landing heavily following an aerial challenge with Spurs goalkeeper Hugo Lloris.
Memories understandably drifted back to the on-field collapse of former Bolton midfielder Fabrice Muamba on the same pitch last season, while the incident was eerily similar to that in the 1982 World Cup semifinal when France defender Patrick Battiston was knocked unconscious after colliding with Germany goalkeeper Harold Schumacher.
While Michu was spread-eagled, and being attended by a number of concerned players, play was allowed to continue by the match officials. That disgusted Swansea, particularly defender Chico Flores and manager Michael Laudrup, and sparked confrontations on the pitch.
"When I saw it I thought, 'Oh hell, he is unconscious, you can't fake a reaction like that,'" Swansea manager Michael Laudrup said. "Still they let the game go on — it is such a poor decision and dangerous as well."
Spurs deserved their win, although they left it late after top scorer Jermain Defoe wasted a couple of good chances and his teammates failed to find any penetration in their build-up play.
When Vertonghen did give them the lead with his first Premier League goal since a summer move from Ajax, Spurs managed to hang on and avoid the concession of late goals that has blighted its campaign this season.
"I think if there was one team to win this game it was us," Villas-Boas said. "We were very patient and persistent in what we were doing."
At the Hawthorns, James Morrison struck efforts against the crossbar twice in the second half for West Brom, whose strong start to the season feels like a distant memory after the team extended its winless run.
"I think the way we've played, we should be kicking on," West Brom captain Chris Brunt said. "Hopefully that can push us on going into Christmas."
Mid-table West Ham will consider it a good point, with its opponent having won six of its previous eight matches at the Hawthorns this season.