The Swans made two changes to their starting line-up as Angel Rangel made his first league start of the season in place of Kyle Naughton, who missed out due to personal reasons.
Meanwhile, Jefferson Montero was given the nod as the Swans aimed to bounce back from defeat at Southampton by claiming a first victory over Tottenham in the Premier League.
Spurs, who beat Manchester City 4-1 last time out, named ex-Swan Ben Davies at left-back while Michel Vorm and former loanee Tom Carroll were on the bench for the visitors.
SWANS: Lukasz Fabianski, Angel Rangel, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Ki Sung-Yueng, Jonjo Shelvey (Jack Cork, 85), Gylfi Sigurdsson (Modou Barrow, 74), Jefferson Montero, Andre Ayew, Bafe Gomis.
SUBS: Kristoffer Nordfeldt, Kyle Bartley, Franck Tabanou, Wayne Routledge, Eder.
TOTTENHAM: Hugo Lloris (capt), Kyle Walker, Toby Alderweireld, Jan Vertonghen, Harry Kane (Mousa Dembele, 80), Erik Lamela (Andros Townsend, 57), Eric Dier, Dele Alli, Nacer Chadli (Clinton Njie, 64), Christien Eriksen, Ben Davies.
SUBS: Michel Vorm, Kieran Trippier, Kevin Wimmer, Tom Carroll.
Spurs arrived in SA1 having won their last Premier League games – including an impressive 4-1 victory over Manchester City last time out – and they started on the front foot at the Liberty with Toby Alderweireld heading over from a corner and Nacer Chadli seeing a low shot saved by Lukasz Fabianski.
However, the hosts regained their composure and took the lead with 16 minutes on the clock.
The move started in defence as Federico Fernandez and Angel Rangel played a neat one-two and as play quickly switched to the other end, Jefferson Montero crossed from the left and Andre Ayew rose high to head past Hugo Lloris for his fourth goal of the season.
Spurs – perhaps feeling aggrieved that the opening goal came against the run of play – responded as Chadli was again denied by Fabianski, before the visitors did eventually draw level.
After Fernandez had fouled Chadli 25 yards from goal, Christian Eriksen stepped up to plant a curling free-kick through the wall and past Fabianski.
But just four minutes later the Swans were back in front, and in bizarre fashion. From an inswinging Jonjo Shelvey corner from the left, Spurs striker Harry Kane attempted to volley the ball clear but ended up miscuing his clearance past Lloris at the near post.
Tottenham then enjoyed their best spell of the game as Fabianski was called into action on three separate occasions.
Kane – looking to atone for his earlier mistake – saw a lot shot well held by the Polish goalkeeper before Eriksen was twice denied by the former Arsenal man.
HALF-TIME: Swans 2 Tottenham 1
Neither side made any changes at the break, but both sides traded good chances within two minutes of the restart.
First it was the visitors who came close to equalising as Harry Kane turned in the box before seeing his effort saved by Lukasz Fabianski, while Jefferson Montero crossed for Bafetimbi Gomis at the other end but the Frenchman couldn’t keep his header down as it flew over the bar.
Spurs made their first change of the afternoon as Andros Townsend replaced Erik Lamela, while Gomis was involved again before the hour mark as he turned his marker 30 yards from goal before driving towards the box and shooting the wrong side of the upright.
Mauricio Pochettino made the second of his three changes on 64 minutes as summer signing Clinton Njie replaced Nacer Chadli, and it had an instant impact as the visitors equalised immediately.
After Dele Alli was tripped by Jonjo Shelvey on the left corner of the penalty area, Christian Eriksen again stepped up to curl a sublime free-kick over the wall and into the top left-hand corner to set up an exciting final quarter of the game.
Swansea, meanwhile, made their first change of the afternoon on 74 minutes as Gylfi Sigurdsson made way for winger Modou Barrow.
But it was Spurs who began to dictate the tempo once more and they came close just moments later as Alli let fly from 25 yards but Fabianski parried his effort away from goal with a good stop.
And Fabianski was called into action once more with ten minutes to play as Townsend cut in from the right before seeing a powerful drive saved by the legs of the Swans keeper.
Spurs then made their third and final change as Harry Kane was replaced by Mousa Dembele for the closing stages, while Jack Cork came on for Jonjo Shelvey for the hosts.
Both sides could have won it in stoppage time as Eriksen – chasing a hat-trick – shot wide of the right-hand post, while at the other end Federico Fernandez was denied a first Swans goal as his header was tipped onto the bar by Hugo Lloris.