They did not register a shot on target in the first half and Chadli's low cross, which was cleared by Sebastien Bassong in the six-yard box, was as close as they came.
It meant that Snodgrass's goal, which gave Norwich a deserved breakthrough in the early stages of the second half, was enough to earn the points.
Defeat bitterly disappointing - Sherwood
Ricky van Wolfswinkel stole possession from Nabil Bentaleb just inside the Spurs half and found Johnson, whose through-ball released Snodgrass. The Scotland international held off Danny Rose and curled his low shot beyond Lloris from the edge of the area.
Spurs finally started to pose a threat but a combination of poor finishing and fine goalkeeping from Ruddy kept them at bay.
Adebayor stole possession from Bassong to go clear but a heavy touch allowed the goalkeeper to come out and save at his feet.
Sherwood introduced Roberto Soldado in place of Paulinho and the Spaniard missed two good chances within two minutes of coming on. First he lashed his shot wide from 10 yards after Adebayor's neat lay-off, before glancing a header wide from Aaron Lennon's right-wing cross.
After that, Norwich missed a succession of chances to double their lead.
Relief for Canaries
Victory was only Norwich's second in their last 12 league games
They have taken 11 points in that period and scored six goals
The Canaries have scored just 20 goals in the league campaign - only Crystal Palace and Cardiff have scored fewer
Snodgrass whipped a free kick narrowly wide and Johnson came even closer, crashing his drive off the underside of the bar. Then Nathan Redmond was denied by Lloris in the follow-up before substitute Gary Hooper's cut back was just behind Alex Tettey, who was well placed six yards out.
Tottenham had one final chance to salvage a point when Chadli was picked out by Mousa Dembele, but Ruddy was there again to make a brave save.
The result moved Norwich four points clear of the bottom three, while Spurs are now six points off fourth-placed Liverpool.
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