Varney began a thrilling Barclays Premier League contest with a stunning volley after just three minutes at Bloomfield Road and Harewood added a second just before the interval.
Kevin Doyle set up a tense finish after Nenad Milijas hit the post for Wolves in a fine second-half response but the hosts held on.
Prince William, taking time out from his wedding preparations, was among the 15,922 crowd with a number of his friends.
He may have enjoyed the game more than the Wolves supporters who, despite their side's spirited showing after the break, booed their team off the field.
The result leaves them entrenched in the bottom three after a run of nine defeats in 11 games.
Source: PA
Source: PA