Varney set up a thrilling 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.
Blackpool had gone into the game with the worst home record in the league but they looked sprightly from the onset against the team with the worst away form.
Wolves were also looking to keep a clean sheet for the first time this season but their plans were in tatters almost as soon as the game had started.
Blackpool were buoyed by the presence of inspirational captain Charlie Adam after an injury scare but their stunning opener had nothing to do with the Scot's creativity.
Varney, wide on the left, chested a long Ian Evatt ball past Kevin Foley and watched it bounce before unleashing an inch-perfect 25-yard shot which looped over Marcus Hahnemann and dipped under the crossbar.
The visitors tried to respond but George Elokobi's shot was blocked.
Harewood tested Hahnemann with a 30-yard shot but the American saved comfortably low down.
Wolves began to enjoy some possession but Blackpool got numbers back.
Adam headed away a corner from under his crossbar and goalkeeper Richard Kingson, playing in place of injured first choice Matt Gilks, was not worried by a header from Christophe Berra.
Doyle also headed wide of the post for Mick McCarthy's side.
McCarthy was clearly not happy with the performance of Foley, who had been shifted infield soon after Varney's goal with Michael Mancienne moving to right-back.
With less than half an hour gone Foley was taken off by McCarthy and replaced by Milijas.
Hahnemann had a moment of uncertainty when he spilled a long-range Evatt shot but there was no danger and he recovered.
The incident failed to jolt the keeper into life and another lapse of concentration allowed Blackpool to double their lead.
Hahnemann came out to claim a David Vaughan corner but missed the ball and Varney headed down.
Harewood was on hand to stab towards goal and the ball found its way across the line despite the last-ditch efforts of Matt Jarvis.
The visiting fans turned their frustration on the team and chanted, 'What a load of rubbish' at half-time.
As a result, Wolves started the second period in determined fashion but David Jones sliced a good chance wide.
Blackpool continued to attack themselves and DJ Campbell beat Berra in the box but failed to find anyone with his cross.
The approach of both sides made for a really open contest and Doyle twice went close, first dragging a shot across goal and then picking out Kingson.
Milijas went even closer after a powerful run down the middle, striking a left-foot shot which beat Kingson to his left but rebounded to safety off the post.
Milijas tried his luck again moments later but blazed over.
Blackpool pieced together another good move with Adam playing Varney through but the on-loan Derby forward shot narrowly wide.
Jarvis pulled the ball back for substitute Sylvan Ebanks-Blake in the six-yard box but it seemed Wolves' luck was out as Vaughan deflected his shot wide.
Wolves continued to press and were finally rewarded five minutes from time as Doyle headed home at the far post from an Elokobi cross.
Jones went down in the area as Wolves pushed for an equaliser in the dying moments but referee Mark Clattenburg was unimpressed.
Campbell spotted Hahnemann out of goal in injury time but his effort from inside his own half stopped short.
Wolves had time to win one last corner but the whistle blew as soon as it was taken.