After a lacklustre first half, Norwich took the lead just 83 seconds after the break when Snodgrass picked out the bottom corner from the edge of the area.
The hosts could have had more but in the end one was enough to claim victory and climb away from the Premier League's bottom three.
Here, Sports Mole dissects the action at Carrow Road.
On target: 3
On target: 2
Was the result fair?
Without a doubt. You can ignore the dud first half and just focus on the second, where Norwich were excellent and should have had at least two or three goals. Spurs had chances themselves but for a team challenging in the top four, it was a hugely underwhelming display from the London side.
Canaries chief executive David McNally had suggested that Hughton could be on his way if Norwich put in a limp display against Spurs. The team did completely the opposite and at full time McNally was in tears in the crowd. Spurs didn't bring their best, but Norwich didn't let them play. The hosts' midfield was especially good and the former Leeds duo of Snodgrass and Bradley Johnson in particular shone. Today's result will be a huge boost to the club, and they will now go into an easier-looking run of games full of confidence.
Seven of today's starting XI also started against Dnipro in the Europa League on Thursday and perhaps weariness played a part in Spurs' uninspiring display. Previously in-form striker Emmanuel Adebayor barely had a sniff up front while in midfield there was very little spark from the likes of Paulinho and Moussa Dembele. Defensively, it was the same four who started in Ukraine and although they were fine in the first half, they looked ragged in the second and started committing plenty of unnecessary, impatient fouls. As well as the return leg against Dnipro, which they are 1-0 down in, coming up, fixtures against Arsenal, Chelsea and Liverpool are also on the horizon for Tim Sherwood's side in a nasty month ahead.
Sports Mole's man of the match
Bradley Johnson: It was always going to be Snodgrass or Johnson but we're giving it to Johnson for his excellent second-half display. He provided the assist for Snodgrass's goal and then came ever so close to one of his own with a rocket free kick that thundered down off the crossbar and onto the goalline. It deserved to bounce over the line.
Roberto Soldado was brought off the bench by Sherwood for a goal and he had a perfect opportunity to equalise seconds after being introduced, but sliced his shot nastily off-target from inside the area.
Craig Pawson had a fine game with the whistle, handling the increasingly-frustrated Spurs players and generally refereeing the contest well.
Norwich: As mentioned above, Norwich now have an enticing run of fixtures and don't face a top-six side for the next seven games. Hughton will know that they have to pick up points in those games as they finish the season with games against Liverpool, Manchester United, Chelsea and Arsenal. Next up is a trip to Aston Villa on Saturday.
Spurs: Sherwood will want to get back to winning ways when they host lowly Cardiff in six days' time.