A bitterly cold night at Molineux was warmed up after 35 minutes by the Spain international's thunderous 18-yard strike.
The hosts were much the better side on the night against a disjointed Palace team which included nine changes and saw talisman Wilfried Zaha start the tie on the bench as goalkeeper John Ruddy, one of two changes made by Wanderers, was never troubled.
After a slow start to the match, Wolves should have taken the lead after 12 minutes but Fabio Silva somehow managed to head the ball over the crossbar from eight yards out following some good work down the left by Pedro Neto.
Jack Butland was the first goalkeeper to be tested midway through the first half, getting down well to his left to push away Nelson Semedo's low strike, following a driving burst forward by the full-back.
Wolves had seen a lot of the ball and made their dominance count after 35 minutes through Traore's superb strike.
The 24-year-old skipped past Eze out wide on the right with a lovely piece of skill before shifting the ball onto his left foot and powering a shot beyond Butland from the edge of the penalty area.
The Palace goalkeeper got a hand to the ball but there was too much power on the shot for him to keep it out.
Silva missed the target again with another free header at the start of the second half, this time glancing his effort wide from a Neto corner.
Palace then enjoyed their best spell of the game, putting Wolves under pressure but without troubling goalkeeper Ruddy.
At the other end Butland made a top save to keep his team in the tie, showing good reactions to deny Leander Dendoncker.
Batshuayi saw a looping shot sail over the crossbar before Palace boss Roy Hodgson introduced Zaha for the final 20 minutes.
The visitors immediately looked more dynamic as Zaha jinked his way to the byline and teed up Batshuayi, but Conor Coady made a last-ditch block to avert the danger.
Wolves went close on the counter-attack with 10 minutes remaining as Neto sent a shot narrowly wide after Ruben Neves' break from defence.
Palace applied some late pressure as they looked for the equaliser but, as was the case all night, they lacked ideas and cohesion in the final third of the pitch.