Wolves had won just once in nine games at Molineux before tricky winger Kightly inspired them to a timely success that has given added impetus to their play-off push.
Kightly, who has made the step-up to the Championship from Conference side Grays with remarkable ease, fired Wolves ahead with his fourth goal of the season and then set-up Stephen Ward's decisive strike in the 40th minute.
Wolves were cruising at 2-0 but ultimately made hard work of their success after substitute Chris McCann handed Burnley a lifeline at the start of the second half with only their second goal in seven away games.
Burnley carried far more of a threat after the half-time introduction of McCann and Kyle Lafferty but by then the damage had been done.
Their misery was summed up three minutes from time when Steven Caldwell rattled the crossbar with his header.
They have now won just one of their last 17 games and early season hopes of a promotion challenge have given way to fears of getting sucked into the relegation battle.
The dye was cast for Burnley as early as the fifth minute when Kightly headed Wolves in front. It would have been harder for him to miss as it was a pin-point cross from Jackie McNamara that he converted from close range.
Ironically, Burnley's best spell followed the goal with Joey Gudjonsson firing over, Wolves old-boy Ade Akinbiyi seeing his drive blocked and their strong claims for a penalty being rejected when McNamara appeared to handle Wade Elliott's cross.
It all proved to be a false dawn for the Turf Moor outfit and they were lucky to survive until the 40th minute before falling further behind.
Kightly and Andy Keogh were both denied by Danny Coyne but Burnley had no answer to the trickery of Kightly.
There initially appeared to be little danger when he collected the ball on the halfway line.
Burnley made the mistake of allowing him to run clear and, when he fed Ward, the Irishman completed a smart piece of play by poking his shot beyond Coyne.
That should have been game over, but Burnley were revived after the interval and were rewarded in the 53rd minute when McCann latched on to a dreadful error from Seyi Olofinjana to drill a low drive past Matt Murray.
Unfortunately for Burnley they could not find another way through and Olofinjana should have made up for his earlier error when he headed wide when well placed in the 68th minute.