Tottenham's new signing Moussa Dembele had come off the bench to put Tottenham in front in the 68th minute with a fine goal but it was a rare bright spark in an otherwise limp performance from the hosts.
Indeed, Spurs needed Brad Friedel to be in top form between the sticks as he made a number of fine saves as Norwich boss Chris Hughton, who spent 28 years at Tottenham as a player and a coach, was rewarded with a gutsy display from his troops.
Snodgrass levelled in the 85th minute but there was still time for more disappointment for Spurs as substitute Tom Huddlestone was sent-off for showing his studs while going in for a 50-50 ball just before the end.
Tottenham had plenty of possession in the opening 45 minutes but looked devoid of ideas and imagination, and if anything the hosts were lucky to go in at half-time level.
Norwich were sitting back and looking to hit on the counter-attack but they had the two best chances in the opening period and if it wasn't for the exploits of Friedel on two separate occasions they would have taken the lead.
After just nine minutes the American keeper tipped Russell Martin's header onto the crossbar after the Tottenham defence failed to deal with a fine Snodgrass free-kick.
Then just two minutes from the break Snodgrass himself came close, again from a header, but Friedel somehow managed to shift position and make a super save from point blank range.
Tottenham on the other hand failed to create one clear cut chance in the opening 45 minutes, with a fizzing left foot shot from Gareth Bale on the half hour being their best effort, but while that shot had plenty of power, it was straight enough that John Ruddy was able to punch it away.
Villas-Boas reacted at the break by bringing on £15m new signing Dembele for Sandro and Tottenham had a brief promising spell just after the break with another summer signing Gylfi Sigurdsson catching a volley clean that had to be saved by Ruddy. Sigurdsson would be substituted for Emmanuel Adebayor soon after.
Despite the Tottenham changes though, Norwich once more settled into their counter-attacking style and continued to manufacture chances of their own.
Grant Holt headed a half chance over in the 51st minutes and then just after the hour, Friedel had to make another good save to push away a low Anthony Pilkington effort.
Spurs fans finally had something to cheer about in the 68th minute though when a moment of class from Dembele put them in front. The Belgian tricked Jonny Howson on the edge of the area with a lovely little drag back and then fired a low shot expertly into the net.
Tottenham might have hoped to kick on after that but again Norwich crept back into the game.
Huddlestone was brought on for Jermain Defoe to try and shut up shop but Norwich got their leveller five minute before the end as Martin and Holt won successive headers from a cross before the ball fell for the impressive Snodgrass to expertly dispatch a finish from just inside the box into the corner of the net.
Neither Clint Dempsey or Hugo Lloris were signed by Tottenham in time for this game but while they could have done with the former against the Canaries, their man between the sticks certainly wasn't the problem as Friedel had to make one last save in stoppage time after Holt's back-heel set up Bradley Johnson for a powerful shot on the edge of the area.
That late effort came when Tottenham were down to 10-men.
Whether the red card was merited is open to debate but what is undisputable is the fact that Norwich were full value for their point and that Villas-Boas will soon be under pressure if performances, and more importantly results, do not quickly improve.
- Brad Friedel
- Moussa Dembele