The visitors, who were without Harry Kane, broke the deadlock on 11 minutes courtesy of a sublime strike from Christian Eriksen that sailed into the top corner.
Spurs thought they had doubled their lead on 24 minutes when Son Heung-min found the back of the net, however, the strike was ruled out by the Video Assistant Referee (VAR) for offside.
Eriksen nearly doubled Spurs' lead with another spectacular effort on 37 minutes but goalkeeper Kristoffer Nordfeldt produced a superb save to push the effort onto the crossbar.
Erik Lamela eventually got Spurs' second goal just before the break with a fine right-footed effort from the edge of the box that left Nordfeldt with no chance.
The Swans looked more threatening in the early stages of the second half with Martin Olsson and Tammy Abraham forcing Michel Vorm into a couple fine saves.
However, Spurs added a third goal in the 63rd minute as Lucas Moura teed up Eriksen, who drilled the ball home from the edge of the box.
That goal seemed to have knocked the last remaining wind out of Swansea's sail as the north London outfit were in full control for the final 20 minutes of the half.
Despite Spurs' domination, 3-0 was how the score remained as the visitors moved one step closer to securing their first piece of silverware since 2008.