Byram, who is out of contract at the end of the season and involved in a dispute over a new deal, cancelled out Benik Afobe's 10th-minute opener on the stroke of half-time
Stuart Dallas then gave Leeds a 51st-minute lead with Byram increasing their advantage on the hour before Nathan Byrne reduced the arrears nine minutes from time
It was a stunning turnaround for Leeds who had to weather a first-half storm before Byram struck
The win gave them some crucial breathing space above the relegation zone as Wolves dismal home continued
Kenny Jackett's side have now failed to win in front of their own fans in six games - their last success at Molineux coming against Huddersfield Town back on October 3
Leeds were inches away from taking a seventh-minute lead following a spectacular effort by Dallas who rattled Carl Ikeme's right-hand post from 25 yards after a knockdown by Chris Wood
Wolves should have capitalised on that let-off seconds later when a jinking run by Jordan Graham teed up Afobe only for the former Arsenal trainee to drag his shot across the face of goal
Fortunately for Wolves that proved to a sighter for Afobe who was more clinical in the 10th minute to break the deadlock when he raced on to a nod down by James Henry and this time made no mistake from 10 yards as he rolled a low shot past Marco Silvestri
Afobe was proving to be a constant threat to the Leeds backline and only a well timed challenge from the United skipper Liam Cooper prevented him from latching on to a Graham cross
After two quick corners in succession, Afobe was then picked out by captain Danny Batth in the 27th minute only to see his shot on the turn fly just wide of the post
Wolves' failure to convert all that pressure came back to haunt them on the stroke of half-time when Leeds grabbed a unlikely lifeline - and gave a sign of what was to come
Byram exchanged passes with Wood on the edge of the area and when he collected the return he stabbed the ball past Ikeme from 12 yards
Wolves still looked to be reeling from that blow at the beginning of the second half as just seconds after the restart Souleymane Doukara fed Wood and it needed a good blocking save from Ikeme to prevent the New Zealand international giving Leeds the lead
But that only proved to be a brief escape for Wolves as the impressive Doukara set-up Dallas who surged into the area before beating Ikeme at his near post
Shell-shocked Wolves would then have slipped further behind in the 55th minute only for Ikeme to pull off a stunning point blank save from Wood's header - and then repeat the feat three minutes later when the former Leicester City marksman was denied from seven yards
But their luck ran out on the hour when Charlie Taylor's left-wing cross flew to the far post where Byram made no mistake with a well-placed header
Leeds looked set to cruise to victory after Byram gave them a two-goal cushion but Wolves rallied and Byrne gave them hopes of a comeback when he converted Graham's looping cross from the edge of the six-yard box
Source : PA
Source: PA