The England Under-20 international striker, who is on-loan from Chelsea, pounced after 37 minutes as in-form Wolves extended their unbeaten run to 10 games - and gained some revenge for their defeat in the play-off semi-finals to Norwich last season.
The visitors have now lost their last four away games and their problems away from Carrow Road are casting a cloud over their latest promotion bid.
And they would have slipped to a heavier defeat but for an impressive display by goalkeeper Robert Green.
While Wolves were indebted to 19-year-old Cole for breaking the deadlock, he had performed heroics in his own area just 60 seconds before his goal to prevent Norwich taking a shock lead in the one real attack.
Following a corner from Phil Mulryne, Cole blocked a header from former Wolves' striker Iwan Roberts on the line before deflecting away a follow up shot from Paul McVeigh.
Having kept Wolves on level terms, he then showed his predatory instincts in the opposition area to earn Wolves their 36th minute breakthrough.
Winger Mark Kennedy, who caused Norwich problems all afternoon down the left flank, whipped in a cross that was fired goalwards by Kenny Miller.
Goalkeeper Robert Green saved Miller's shot was but was left hopelessly out of position for the follow up from Cole who was able to thread his low drive home through a crowded goalmouth from 12 yards.
It was no more than Wolves deserved as the heroics of Green had prevented them taking the lead when he saved from Kenny Miller, Alex Rae and Kevin Cooper.
Boosted by their goal nine minutes before the interval, Wolves began the second-half at a frantic pace and would have increased their advantage but for more heroics from Green.
He pushed a 46th minute volley from Cooper over the bar and then turned away further efforts from Miller and Cole.