The lads pressed Brighton on the ball and continually won possession in their attacking third in the opening half-hour.
That led to a number of chances and Bongani Khumalo had already clipped the top of the crossbar from 16 yards when Alex Pritchard opened the scoring in fine style with 17 minutes on the clock.
Milos Veljkovic won the ball and it moved left to right through Nabil Bentaleb, Massimo Luongo and Souleymane Coulibaly to Pritchard, who cut inside two defenders before curling left-footed past Casper Ankergren into the far corner.
Pritchard was just too high with a chip from the edge of the box and another slick passing move set-up Luongo, whose 25-yarder brushed the crossbar on the way over.
Brighton levelled with their first serious attack when George Barker failed to connect with Torbjorn Adgestein's cross but Jake Caskey was there to finish for 1-1 after 32 minutes.
The visitors completed the turn around before the break when Caskey curled a beauty into the top corner from 25 yards.
The second half was a much more even affair and the Seagulls had more than their fair share of chances. Smith cleared off the line from Barker and Jonathan Miles acrobatically tipped over from Rodgers.
Pritchard poked just wide on the hour but Brighton forged further ahead minutes later when Barker worked a yard of space and drilled low across Miles into the far corner.
Roland Bergkamp capitalised on a defensive mix-up to roll home the fourth goal 10 minutes from time.
Pritchard was fittingly involved in the final chance as he got to the right byline and found Coulibaly, who was denied at close range by Ankergren.
Spurs XI: Miles; Smith, Khumalo, Uvini, Byrne; Luongo, Veljkovic (Gallifuoco, 64); Pritchard, Munns, Bentaleb (Oduwa, 64); Coulibaly. Unused sub: Granger.