Welbeck capitalised on a deflected cross to hit an incredible overhead kick as Nigel Pearson’s side came from a goal down to secure their first victory since the Premier League restart.
The Canaries have now lost all six of their matches following the resumption, but took the lead through Emiliano Buendia inside the first five minutes at Watford.
Buendia’s strike was Norwich’s first Premier League goal since February 29 and also marked the first time Daniel Farke’s men had taken the lead since that date, although their advantage was short-lived.
Craig Dawson’s header levelled the game six minutes later with his second goal since the break.
In the second half, Watford edged closer to claiming their first win since the restart when Welbeck struck.
The 29-year-old put his side ahead for the first time in the match with the second bicycle kick scored by Watford since the restart – the first was Dawson’s leveller against Leicester.