Jermain Defoe opened the scoring for the visiting team in the 58th minute, before the Welshman added a swift treble to secure a comfortable victory.
The north London outfit went into the game on the back of a goalless draw with Stoke, knowing anything other than a win would see the club slip further behind their contenders for a top four place.
"Great to score goals and my first hat trick in the Premier League but important to get the 3 points," he told Tottenham's official Twitter account.
"All the lads worked hard out there and we knew once we got one we'd get more, we look to Sunderland now."
Bale's manager Andre Villas-Boas was also pleased with the way that his squad took control of the game from the beginning to the end, adding: "It was very good from start to finish, we truly deserved it.
"We deserved it in the first half and it did not happen so we had to keep on concentrating, we deserved to win and it was a great performance."