Spurs broke the deadlock in the 57th minute when Aaron Lennon raced down the right and beat Tim Krul with a low drive from inside the box after being given space by James Perch.
Cheik Tiote, who was lucky not to receive a second yellow for a foul on Luka Modric, then squared up to Younes Kaboul after the midfielder slid in to tackle the defender.
The former Portsmouth player forced his head forward onto Tiote's and although not a clear headbutt, was enough to persuade referee Anthony Taylor to send Kaboul off.
Lennon shot just wide and any hopes of a Newcastle comeback were extinguished with 10 minutes left when Bale accelerated past Steven Taylor before smashing a low angled drive past Krul for his 10th goal of the season.
Source: PA
Source: PA