Bale scored on a free-kick in the fifth minute before Newcastle equalized 19 minutes later through Yoan Gouffran.
In the 78th minute, Bale delivered another piece of brilliance when he scored the match-winning goal on a counter-attack.
The win extended Tottenham's unbeaten streak to 10 matches and temporarily put them into third place ahead of Chelsea.
Here are six things we learned from the Spurs' victory over Newcastle.
Gareth Bale was clearly the man of the match at White Hart Lane on Saturday. The Welshman scored on a brilliant free kick in the fifth minute before scoring the match-winning goal in the second half. Bale's double gave him 13 EPL goals on the season.
With Jermain Defoe out injured, Spurs needed someone to step up and score goals and Bale did exactly that against Newcastle. Bale also created plenty of other chances for his teammates, but none were able to convert his stellar passes into a goal.
One thing that Bale will be wanting to change is his missed shot in front of an open goal in stoppage time.
Bale took the shot with his right foot, which is not his preferred foot, and the ball soared over the wide-open net.
When Emmanuel Adebayor entered the match in the 69th minute, the match became wide open and the Tottenham attack flipped the switch and turned into a threat once again.
Toward the end of the first half and during the first 25 minutes of the second half, the Spurs attack lacked the final touch. When Adebayor entered the match, Clint Dempsey was allowed to move back into the attacking midfield role and the American was able to switch off with Gareth Bale in the attack.
With Bale given more freedom in the attack, Spurs were able to create plenty of chances.
It will come as no surprise to anyone if Adebayor is installed as the permanent forward in the 4-2-3-1 formation until Jermain Defoe returns from injury.
Michael Dawson had yet another fine performance in the back four against Newcastle
Since being installed as a starter at center-back in November, Dawson's play has improved by the match and it has caught the eye of England manager Roy Hodgson, who was in attendance on Saturday.
While the number of blocked shots by Dawson may not show up on the stat sheet, there is no doubt that the Spurs defense would not be as effective as they were against Newcastle if the 29-year-old was out of the starting 11.
Tottenham goalkeeper Hugo Lloris was not asked to do much on Saturday. But when he was called into action, he performed well.
The most important play made by the Frenchman came in stoppage time when he stopped Shola Ameobi from going through on goal and taking a shot.
Ameobi looked like he was going to take a clear chance on goal, but the Spurs keeper came out to disrupt the Newcastle forward and the ball was cleared out for a corner kick.
With his stoppage-time save, Lloris saved Spurs suffering from their second-half conceding curse once again.
Lloris may be called into action on Thursday against his former club, Lyon, in the Europa League, a match where he will surely have to make more than two saves to earn a win for Tottenham.
Yoan Gouffran was the best player who stepped on the pitch for Newcastle at White Hart Lane, and he was forced off with an injury in the 59th minute.
Gouffran suffered a shin injury when Kyle Walker's boot clipped him in the aftermath of a tackle.
With Gouffran out of the match, the Newcastle attack seemed to be shut down until the final minutes.
His replacement, Sylvain Marveaux, only touched the ball 17 times in 31 minutes, which is a horrendous number for a player who was tasked with inspiring the Magpies' attack.
Gouffran's injury status is not known at the moment. But if he is out for a significant amount of time, the Magpies' attack could suffer like it did in the second half against Tottenham.
Tottenham are one of the best clubs in England, and they are giving Chelsea a run for their money when it comes to the third position in the table.
The win over Newcastle extended the Spurs' unbeaten run to 10 matches.
During that span, Chelsea has lost twice and they have given Spurs a sense of belief that they can finish in third place.
With Spurs in excellent form and Chelsea being inconsistent at times this season, there should plenty of belief at Tottenham that they can finish in third place.
What did you learn from Tottenham's win over Newcastle?
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