After laying siege to the Canaries goal in the first half, Spurs finally found the opener 10 minutes after the break when Bale picked up Emmanuel Adebayor's pass to drive under John Ruddy.
Bale then latched on to Luka Modric's pass to sprint 45 yards before lifting the ball over the on-rushing Norwich goalkeeper with a sublime finish to kill off the match 12 minutes later.
The performance may have been slightly ropey in the first half, but the devastating display from Bale highlights just why Tottenham are proving that they should be deemed credible title challengers.
The Londoners, who have a match in hand over all their rivals, will head in to the new year as the capital's top club, and with games against Swansea and West Brom coming up, few would back against Harry Redknapp's men putting more pressure on both Manchester teams over the next few days.
With Chelsea, Manchester City, Arsenal and Liverpool all drawing over the past 24 hours, Tottenham had the perfect chance to put themselves within striking distance of the summit.
They received a boost before kick-off with the news that Norwich duo Adam Drury and Ritchie de Laet, who had begun just five league games between them this season, started at full-back due to Kyle Naughton's suspension and an injury to Marc Tierney.
A speculative volley from Steve Morison gave Brad Friedel an early test, but Redknapp's team soon started to dictate play.
Bale drew saves from Ruddy on two occasions after terrorising De Laet with his searing pace.
Grant Holt somehow managed to escape without a caution for an apparent elbow on Benoit Assou-Ekotto as the left-back attempted to play a one-two with Adebayor on the left.
Replays showed the striker had clearly led with his forearm in attempting to shrug the defender off the ball in a challenge that perhaps merited a red card, but referee Michael Oliver kept his cards in his pocket.
Norwich grew in confidence briefly, but they soon found themselves on the back foot again.
Russell Martin put in a crucial header to deny Adebayor a great chance from six yards after a teasing cross from Kyle Walker.
Norwich appealed for a penalty when the ball struck Younes Kaboul in the box but Oliver waved play on.
Bale slammed a deflected shot just wide, but he was soon presented with another chance thanks to an error from Martin. The Welshman nicked the ball off the dallying defender and charged through clear at goal but he could only blast over.
A superb 50-yard ball from Rafael van der Vaart sent Adebayor free. The striker edged the ball past the on-rushing Ruddy, but he could not recover it to tap home and the ball went out of play.
Another Spurs attack came moments later when Bale got on the end of Modric's through-ball but Ruddy pulled off a good save.
Martin put in a sliding tackle to deny Adebayor, who then blazed over in injury-time as Tottenham's half ended in frustration.
William Gallas slipped on the edge of the box, bringing down Andrew Surman and earning himself a booking as Norwich began the second half with more confidence.
Surman picked himself up and curled a low shot that drifted inches wide, with Friedel scrambling for his far post.
Spurs took the lead 10 minutes in to the second half. Van der Vaart picked out Adebayor in the box, he held the ball up and fended off three Norwich defenders before squaring to Bale who got the ball out from under his feet to shoot under Ruddy after being left unmarked 12 yards out.
Assou-Ekotto found Walker unmarked at the back post after a clever one-two with Modric but the right-back cleared the bar by at least 10 yards with a poor shot.
Adebayor converted Assou-Ekotto's cross soon after but the Togo striker was ruled out for offside.
Bale grabbed his second of the game to make it 2-0 in the 67th minute.
Parker won the ball off Morison and laid the ball to Modric, who sent the Welshman galloping through on a 45-yard dash. Bale kept his composure after a heavy first touch before dispatching the coolest of chips over an on-rushing Ruddy, who dove at the winger's feet in vain.
Adebayor squared for Modric as Tottenham looked for a third but the Croatian could only muster a weak shot that Ruddy gathered easily.
Martin headed wide in injury time as Norwich looked for a consolation, but it never came and Spurs played the rest of the match out comfortably for a vital three points.