Sweden international Martin Olsson was shown a second yellow card after hauling down Rajiv van La Parra just outside the area, and could face further sanction for a light shove on the chest of referee Simon Hooper as the official branded the card.
Olsson's dismissal left Norwich in the lurch for the remaining half-hour, and in the 64th minute Edwards' goal - from a superb Van La Parra cross - earned the hosts all three points in front of over 22,000 at Molineux.
The sides were two divisions apart last season, but Wolves' promotion as League One champions and Norwich's relegation from the Premier League saw the pair clash again, three years after their last meeting in the top flight.
The first half was a cagey affair, with neither side managing to stretch the two goalkeepers.
Andrew Surman had the game's first real chance nine minutes into the second half, but the midfielder was denied by a fine block from Richard Stearman.
Lewis Grabban - signed from Bournemouth in the off-season - tested Carl Ikeme two minutes later but just as Norwich looked to have seized the initiative, Olsson saw red for bringing down Van La Parra as the winger sped down the right-hand side.
While the free-kick from a dangerous position came to nothing, Olsson's angry reaction to the decision could land him in further trouble with the authorities after he laid a hand on Hooper.
Wolves made the man advantage count almost immediately as Edwards timed his run to perfection and glanced Van La Parra's delivery into the far corner with John Ruddy helpless.
The hosts ought to have made the game safe 11 minutes from time but after breaking away down the right, Nouha Dicko's pass was behind Bakary Sako, who was forced to take a touch and then saw his shot saved by Ruddy.
But it mattered little as Wolves' return to the second tier got off to a fine start while Norwich's expected promotion challenge suffered an early setback.
