Scotland midfielder Snodgrass fired the Canaries to just their second win in 12 league clashes, with goalkeeper John Ruddy producing a string of first-class saves to ensure the hosts banked all three points.
Chief executive David McNally has admitted Norwich would be "delinquent" not to keep eyes and ears open for a replacement for embattled boss Chris Hughton ahead of Sunday's game.
McNally's revelation raised rumours Neil Lennon could trade Celtic for Norwich, but this nervy victory may keep Hughton in his post just that little bit longer.
A circumspect first half left the hosts the more frustrated with the deadlock at the break.
Dutch midfielder Leroy Fer would have harboured most of the Canaries' annoyances all on his own, after missing the half's only clear-cut chance.
Fer's chance was positively gilt-edged in fact, the 24-year-old failing to tuck away Martin Olsson's threatening cut-back.
Nathan Redmond sent Olsson in behind Kyle Naughton on Norwich's left flank, and his accurate cross begged for a finish from the penalty spot. The onrushing Fer could not quite arrive in the box quickly enough, though, failing to capitalise on a completely static Tottenham defence.
Spurs struggled for rhythm and pace throughout the half, the visitors as much at fault for their midfield shortcomings as Norwich merited praise for continually hassling them off their stride.
Joseph Yobo's hefty clearance handed Ricky van Wolfswinkel a chance to terrorise the poorly-positioned Michael Dawson on the cusp of the Spurs box. Instead he dallied and was dispossessed with little more than a whimper.
So out of sorts and hesitant before the break, Van Wolfswinkel somehow managed to leave his meekness in the changing rooms.
Straight from the second-half kick-off the Dutchman produced a telling contribution that sparked the counter-attack for the opening goal.
Sneaking up on Bentaleb, Van Wolfswinkel picked the Spurs midfielder's pocket before releasing Bradley Johnson. Snodgrass immediately picked a smart diagonal run in behind the Tottenham defence and Johnson slid him the perfect ball. Snodgrass latched onto the pass, steadied himself and buried a low left-footed strike past Lloris.
The Norwich goal sparked an inevitable Spurs reaction, but Chadli wasted acres of space with a poor cross, before Rose spoiled a fine 50-metre break with a loose pass.
Adebayor then bustled past Canaries centre-backs Bassong and Yobo, muscling a fine opening, but Ruddy raced off his line to slide onto the ball and deny the Togo striker.
Lennon and Adebayor's one-two sent the rangy Spurs forward through on goal again, but once more Ruddy was equal to the challenge.
Spurs boss Sherwood threw Roberto Soldado into the mix, and the switch to a two-man strikeforce almost paid immediate dividend. Adebayor played Soldado through on the inside-right channel, but the Spaniard hit only side-netting.
The former Valencia striker had another clear opening moments later, but headed Lennon's pinpoint cross wide of goal.
Chadli headed back across goal with no team-mate in attendance, then Adebayor could not direct the winger's cross to trouble Ruddy.
Tottenham's increasing threat cranked up the tension, and Ruddy was forced to deny Chadli at point-blank range.
Norwich were not to be denied, though, and rallied once more in the closing 10 minutes.
Johnson's firecracker free-kick smashed the crossbar and then Lloris parried the follow-up from Redmond to safety.
Gary Hooper raced clear and squared the ball across the empty net, but no yellow shirt could provide a finish.
But Norwich held on to secure three points which moved them up to 14th.