The only surprise was that it took them so long to score as they had enough chances to be out of sight before Kightly struck with Rob Edwards twice being frustrated by the woodwork.
It needed Kightly to fire home his fifth goal since his arrival from Grays Athletic in November to seal their success.
Kightly picked up a cross-field pass from Jackie McNamara before drilling home a low drive from 20 yards to finally break the resistance of Leeds.
Leeds, who have failed to win at Molineux since December 1984, had looked on course to pick up a priceless point after a dogged display.
They carried little threat themselves in attack although no-one can criticise their determination and work-rate that has been drilled in to them by manager Dennis Wise.
They noticeably stepped up a gear in the second half after being outplayed for long spells in the first 45 minutes but still lacked a cutting edge in front of goal.
Their best chance fell to Eddie Lewis in the 88th minute who saw his shot tipped over the bar by Matt Murray.
Apart from a three-minute spell, Wolves, were dominant in the first half and should have been well in control.
But a combination of poor finishing, the woodwork and a controversial decision by referee Michael Jones ensured they didn't make their domination pay.
Seyi Olofinjana failed to convert two close-range headers although his first after 22 minutes was well saved by Casper Ankergren.
Andy Keogh also had a shot blocked by Matt Heath before Jones infuriated Wolves by rejecting their penalty appeals.
Kightly cut inside Lewis before going down under a challenge from Rui Marques only for Jones to reject their claims for a spot-kick.
Leeds, who have now lost seven of their last eight away games, were inspired by the let-off and could easily have taken the lead themselves only for Richard Cresswell to miss a sitter.
Robbie Blake whipped in a free-kick that Cresswell lifted over the bar from just two yards.
Blake went close from 20 yards three minutes later before the woodwork saved Leeds when Edwards headed a free-kick from Michael McIndoe on to the post.
Amazingly, Edwards then slammed another McIndoe free-kick against the post in the 56th minute before Kightly came to their rescue.