The visitors came close on 21 minutes when a free-kick from Michael Kightly evaded a host of gold shirts and curled wide of the far post.
Two minutes later, a free-kick from Graham Alexander was not claimed by Hennessey who redeemed himself by blocking the follow-up shot from Martin Paterson.
On the half-hour mark, Paterson fed Robbie Blake and his cross was headed just over the bar by Elliott.
Ten minutes into the second half and with Blake pulling the strings for Burnley, he set up a chance for McCann which was blocked by Hennessey, but striker Paterson could only hit the side-netting with the rebound.
Paterson then rounded the goalkeeper but saw his shot cleared off the line by Richard Stearman.
Paterson then appeared to be hauled down by Stearman on the edge of the six-yard box but referee Oliver waved play on.
Wolves boss Mick McCarthy made a double substitution on 58 minutes as he tried to get his team into the game.
One of those substitutes, Chris Iwelumo, did have a chance but didn't connect cleanly enough to beat Brian Jensen.
Burnley substitute Kevin McDonald came close with his very first touch, curling a shot just wide from the edge of the box.
Wolves did have a chance of an equaliser 13 minutes from time but Stearman headed Kightly's free-kick wide of the target.
Goalscorer McCann had a further opportunity when he received a pass from Alexander but put his shot on the roof of the net.
The win was fully deserved by the home team, who should have won by more than a one goal margin and in Blake had the game's most dominant individual.