Bale flicked in the opener when it was lifted over the top by Serge Aurier before the right-back teed him up to thump in the third in the second half.
The Welsh international was played in by Son Heung-min on the break for his second - a thumping strike which flew into the top right corner.
Son rounded off a dominant Spurs performance when he curled in a superb fourth goal.
The South Korean also had a goal disallowed for offside five minutes into the second half.
Bale said he was "feeling good" after starting back-to-back Premier League games.