The out-of-form Benik Afobe handed the home side the lead at Molineux, but the Leeds youngster found the back of the net in the 44th minute to restore parity.
Afobe, who has been strongly linked with Norwich City and Newcastle United over recent days, had found the net just once in his previous nine outings prior to his 10th-minute strike against Steve Evans's men.
However, with a little more luck on their side, it would have been the visitors that celebrated the opening goal. Stuart Dallas's volley left Wolves goalkeeper Carl Ikeme rooted to the spot, but the Northern Ireland international's effort crashed against the upright.
Sixty seconds later Afobe shot wide when well placed, but the 22-year-old made no mistake with his next opportunity. He raced through to collect James Henry's flick-on, before firing past Leeds keeper Marco Silvestri. It was the former Arsenal man's first home goal for Wolves since the clash with Huddersfield on October 3.
As the half wore on Afobe shot just off target, while a curling effort from playmaker Jordan Graham forced Silvestri into routine action.
But, having dominated the last five minutes of the half, Leeds made it count when Byram got the better of Danny Batth and then slotted in his first league goal of the season.