The Welshman helped himself to his 21st goal of the season, powering in Sigurdsson's cross, before the Icelander and Vertonghen added a goal apiece to put Spurs in control
Sigurdsson picked up where he left off against Arsenal on Sunday, finding the Welshman with a teasing cross, before pouncing on Samir Handanovic's parry to double the lead. Vertonghen added a third with a powerful close-range header in the second half.
It didn't take Tottenham long to stir the home crowd as Sigurdsson collected another assist after good work on the left flank. His inswinging cross in the sixth minute was met by Bale, who climbed higher than Esteban Cambiasso and placed a header firmly into the bottom corner for his 21st goal of the season.
Under the lights, Tottenham was flying. Sigurdsson, reveling in another start under Andre Villas-Boas, was sharpest to the loose ball after Handanovic made a mess of Jermain Defoe's low strike and tapped home to put Spurs 2-0 up after just 18 minutes.
Though Inter threatened in brief patches, the first 40 minutes were all about Tottenham's control of the game as the English club played patiently but effectively, slicing through the middle via Mousa Dembele and Scott Parker's driving runs.
Bale, who was booked for diving and will miss the second leg, flirted with the idea of stealing the headlines, but didn't need to and for swathes of the first half was regularly just a link between midfield and attack.
A driving run and shot wide on the hour were as close as he would come to getting a second. He did help add a third goal though as his corner was powered home by Vertonghen, who earlier had missed a golden chance from a similar position.
For Andrea Stramaccioni's side it could have been a different story had Ricky Alvarez, once linked with Arsenal, not dragged a golden chance wide of Brad Friedel's far post. The 24-year-old looked the most likely man to find an away goal in the first period but his finishing was too wild to trouble the Spurs goal.
As the game entered the final 30 minutes Defoe, who returned to the lineup in place of the injured Emmanuel Adebayor, almost made it 4-0, ruing Handanovic's fortunate save with his elbow as he swivelled and snapped a shot at goal. He would later waste a four-on-two break looking for a shot instead of passing to the onrushing Kyle Walker or Bale.
Lennon had been diligent in his work on the right flank but after another surging Parker run collected the ball in the Inter half and charged at the backline. His nutmeg on Christian Chivu was impressive, but Handanovic was out quickly to smother the finish.
Inter was not buried yet though and after introducing Fredy Guarin to proceedings drew Friedel into a vital save as Cassano was played in on goal from a quick free-kick.
As Inter pressed higher and more desperately, space began to open and substitute Lewis Holtby should have done better with his 20-yard effort, but the home side remained in control and will take a huge advantage back to Italy.