Thomas Frank's Championship promotion-chasers headed into the match bolstered by a 16-match unbeaten run and victories over four other Premier League sides in this season's competition, but Sissoko's 12th-minute header punctured any early enthusiasm.
The visitors posed enough questions of Spurs in their usual eloquent style and Ivan Toney had a 63rd-minute header disallowed for offside.
Son then streaked clear of their defence to hammer home his 16th goal of the season and grant Tottenham boss Jose Mourinho his latest shot at silverware.
