The big striker scored the first and third in each half, with Chico Flores knocking into his own net and Wilfried Bony replying for Swansea.
It was our fifth successive away win in the Premier League, the first time we've achieved five away wins on the trot in league action since the great double side of 1960-61 - that run in October, 1960.
Tim Sherwood made one change to last time out against Crystal Palace, drafting in Nacer Chadli in place of Roberto Soldado, offering an extra man in the middle of the pitch against a renowned passing team.
Just two minutes in Swansea cut through our defences when Alejandro Pozuelo knocked through for Wilfried Bony to charge through on goal. Thankfully his touch was heavy and Hugo Lloris was quickly off his line to thwart. Pozuelo continued to cause uncertainty in a hesitant back line three minutes later, holding off challenges to present Jonjo Shelvey with a good shooting chance that he fired over.
On 13 minutes Shelvey stung the hands of Lloris, with the goalkeeper making an excellent stop to palm away his piledriver from outside the area.
Inbetween times, control in the game was growing, with Mousa Dembele and Christian Eriksen beginning to exert an influence and Emmanuel Adebayor a lurking menace.
But it was Bony with the next shot, trying his luck from outside the area after a tangle with his markers, then again on 24 minutes when he rattled the crossbar.
There was a good chance on the counter when Adebayor sent Walker scurrying clear, but his next pass in the direction of Chadli lacked a little in power and was intercepted. On 32 minutes Bony forced a superb save from Lloris from inside the area - little would the keeper have known that the flag was raised to his left.
Against the run of play - and certainly chances - the lead was taken on 34 minutes when Aaron Lennon and Eriksen combined, with the Dane whipping in a dipping cross that Adebayor was perfectly in position to nod home in front of goal.
The lead should have been doubled moments later when Danny Rose picked out Chadli in the area but, with time and space, the Belgian aimed high. Adebayor then rocked Gerhard Tremmel back on his heels with a fierce volley from a Vlad Chiriches flick-on. The momentum was building as the clock ticked towards half-time.
Kyle Walker denied Wayne Routledge a route through on goal in stoppage time.
On 52 minutes the lead was doubled and Walker played a big part. The full-back was on the run when Michael Dawson strode forward and played a precise ball into his path. Walker drilled across the face of goal and it was Chico Flores who made contact and diverted past keeper Tremmel.
After a period of picking Swansea off and playing on the counter-attack, the home side mustered up a purposeful attack of their own and it was Bony again who smashed goalwards, with Lloris again in position to block.
Gylfi Sigurdsson took over from Chadli just before Chiriches took a blow to the face from the head of Bony in a coming together. Dembele then worked his way clean through on goal but, instead of playing in Adebayor to tap into an unguarded net, he went solo and rolled the ball wide - much to the dismay of Adebayor.
Ade certainly cheered up a minute later with 71 on the clock when Rose did elect to pass to him in front of goal and the big striker duly slotted past Tremmel to make it three and a salute to the travelling Spurs fans.
The lead was reduced on 77 minutes after a failure to clear lines on several occasions resulted in Bony striking past Lloris to make it 3-1. Tim's next move was to replace Lennon with Kyle Naughton, with Walker pushing forward.
Tremmel made a smart block to deny Sigurdsson a goal on his return to the Liberty Stadium and Adebayor almost latched onto Chiriches' through ball for a hat-trick chance. Five minutes added time passed without concern and we had another three points in the bag on our travels.
Swansea: Tremmel; Rangel, Flores, Williams, Davies; Routledge, Amat, Britton, Pozuelo, Shelvey (Lamah, 51); Bony. Unused subs: Cornell, Taylor, Tiendalli, Vazquez, Richards, Donnelly.
Spurs: Lloris; Walker, Chiriches, Dawson, Rose; Lennon (Naughton, 79), Bentaleb, Dembele, Eriksen, Chadli (Sigurdsson, 71); Adebayor. Unused subs: Friedel, Capoue, Holtby, Defoe, Soldado.
Goals: Swansea - Bony (78). Spurs - Adebayor (35, 71), Flores own goal (53).
Yellow cards: Swansea - Amat, Bony. Spurs - Rose.
Referee: Mr M Atkinson.