Rafael van der Vaart put the hosts ahead in the first half with a splendid finish, but the Dutchman's effort was cancelled out by another good goal from Gylfi Sigurdsson but two late headed goals from Emmanuel Adebayor secured a crucial three points for Harry Redknapp's men.
The victory means Spurs now trail their north London rivals by just one goal and the Welshman is now looking for the team to climb back above Arsene Wenger's men.
He told Sky Sports: "We knew the results yesterday, we knew what a massive win it was for QPR to beat Arsenal. It gave us an opportunity to get back level with Arsenal and hopefully go above them."
Before the clash at White Hart Lane, Spurs had only won one out their last six Premier League ties, the 22-year-old believes the run was down to luck but did admit the win was crucial.
"We've been playing well," he said. "We've had quite a lot of bad luck but we showed what we can do on the pitch here today against a great footballing side like Swansea, and got the vital three points to put the pressure on the others."
Despite the 3-1 scoreline Tottenham were, at times, made to work very hard in defence. Scott Sinclair in particular showed moments of magic for the visiting side.
The former Southampton man applauded Swansea's brand of football but suggested that Spurs hit top form on the day and took their chances well.
He continued: "The way they play the ball is just unbelievable and it's full credit to them. They've been fantastic this season but we showed our true class today.
"We showed what attacking prowess we [have] and we punished them when we could."
The London outfit had been flying earlier in the season but their recent dip in form led many to write off their Champions League qualification chances.
However the winger believes that the side are back to their best, insisting that they are confident of ending the season positively.
He added: "We were just saying, me and Younes [Kaboul] 'We're back now'. We feel like we're playing well.
"I think at Stoke was the tuning point, when we got the last minute equaliser. The confidence is building and [we're] ready for our run-in."