Hosting Spurs started the brighter of the two sides, with Louis Saha forcing John Ruddy into a low save.
Pilkington went close again in the 29th minute, but Friedel got the better of the midfielder on this occasion.
With Norwich on top, Spurs found the equaliser in the 33rd minute. Jake Livermore was the creator, slotting a ball through to Jermain Defoe for the England international to chip in his 16th goal of the season.
Up the other end Norwich skipper Grant Holt picked out Bradley Johnson in the 56th minute, but the midfielder sent his effort into the side netting.
Just after the hour mark Bale went close to putting Spurs in front for the first time when his curling effort from the right side of the box struck the underside of the crossbar before being cleared to safety.
Moments after Bale had hit the woodwork, the Canaries took the lead again. Elliott Bennett collected possession 20 yards from goal and sent a shot past a motionless Friedel in the home goal.
Spurs pushed forward for their second equaliser of the afternoon, but the Norwich rearguard held firm.
The loss means that Spurs remain fourth in the Premier League table.