Early in the ninth minute Harry Kane had an opportunity to let rip off a free-kick from 40 yards out as it dipped low to produce a fine save from Lukasz Fabianksi.
Moments later Moussa Sissoko slipped Son Heung-min through on goal but his from an acute angle was saved by Fabianksi for a corner.
The first half went on as neither team could produce any clear goal-scoring opportunities despite Tottenham with majority of the possession.
Swansea did close on the stroke of halftime as defender Mike van der Hoorn headed Tom Carroll's cross just over the crossbar moments.
13 minutes minutes into the second half, Son had a chance on goal however his close-range shot was saved, Sissoko then crossed for Kane who struck the crossbar from 12 yards out moments later.
Spurs kept piling on the pressure on Swansea as and Fabiasnki was kept busy as he produced a good save to keep out Son's volley in the 66th minute
Spurs carved out another chance in the 808th minute when Kane received and turned to unleash a long range shot which narrowly missed the target.
Substitute Serge Aurier missed an opportunity to steal the game in stoppage time as he powered past the Swansea defense only to rush his shot wide from close range.
For all of Spurs dominance Pochettino's men struggled to get their first win at the Wembley Stadium.