Bale had only been on the pitch for three minutes when he met Sergio Reguilon's cross with a firm header in the 73rd minute to clinch his side's first home Premier League victory of the season.
Harry Kane had put Spurs ahead with a 13th-minute penalty after he had been fouled on the edge of the area by Adam Lallana.
It was his 149th Premier League goal, placing him joint-10th in the all-time scorers' standings.
But Tariq Lamptey equalised with his first top-flight strike on 56 minutes.
Erik Lamela and Kane then each hit the post before Bale struck.
Spurs have 14 points, two behind leaders Liverpool.
Brighton, without a win in five league matches, remain 16th in the table with five points.
Spurs: 8 Nov v West Brom (A)
Brighton: 6 Nov v Burnley (H)
Budweiser King of the Match: Harry Kane (TOT)