The pacey Welsh international took his league tally this season to seven goals, lifting third-placed Spurs, who have a game in hand on the two Manchester clubs, up to 38 points from 17 matches.
Bale drilled home the opener on 55 minutes after fine trickery in the box by Emmanuel Adebayor who bamboozled three Norwich defenders with neat footwork before laying off for the winger to take a touch and pick his spot past keeper John Ruddy.
Bale's blistering run from halfway and neat chip over Ruddy doubled the lead 12 minutes later and sealed a sixth away league win of the season for the London side.
"Gareth's an amazing player isn't he?," Spurs manager Harry Redknapp told Sky Sports.
"I told him and Rafa [Rafael van der Vaart] to play where they wanted... I gave them a licence to play. When he [Bale] picks it up and runs at you he is unplayable."
Spurs dominated throughout against a hard-working but limited Norwich side at Carrow Road.
"It was a good performance," added Redknapp. "When you are up there you have to keep picking up results."
Earlier, Arsenal missed the chance to go fourth after a fine performance from Wolverhampton Wanderers goalkeeper Wayne Hennessey helped secure a 1-1 draw at Emirates where the visitors finished with 10 men.
"It is very frustrating. You won't play many draws like that in a season but sometimes it can happen," Arsenal manager Arsene Wenger told reporters.
"We still lack a bit of maturity. The way I have seen the game today it will be one draw out of 50 but it was that one today."
Arsenal, who remained fifth on 33 points, had looked set for a comfortable afternoon when Ivorian striker Gervinho ran on to a Yossi Benayoun pass to round Hennessey and break the deadlock after eight minutes.
SCUFFED SHOT
Wolves, one place above the relegation zone, levelled against the run of play seven minutes before half-time, their leading scorer Steven Fletcher reacting quickly to head in Stephen Hunt's scuffed shot from the edge of the area for his seventh league goal of the season.
Arsenal piled on the pressure after the break but found Hennessey in outstanding form.
The Wales goalkeeper made a string of fine saves, tipping over a Robin van Persie free-kick midway through the second half before foiling defender Per Mertesacker from point-blank range.
The hosts failed to capitalise when Wolves went down to 10 men with 15 minutes left after Serbia midfielder Nenad Milijas's straight red card for a late challenge on Mikel Arteta.
Hennessey again came to the rescue for Mick McCarthy's side late on when Thomas Vermaelen got through on goal.
"Wayne Hennessey was fantastic. I think he is one of the best goalkeepers in the league and he proved that today," said McCarthy.
The match was put back 24 hours because of a strike on Monday by London Under
