The result left United third in Group E, behind Real Sociedad and early leaders Sheriff Tiraspol, who beat Omonia Nicosia 3-0.
The winners of the group stage, which begins from September 8, will advance directly to the round of 16 that will take place from February onwards.
The Polish striker scored his first goal in competition for Barcelona when he opened the scoring in the first minute.
Second-half goals by Carlos Vinicius and Giovanni Lo Celso earned Tottenham a 2-0 win over Royal Antwerp as they leapfrogged the Belgians who had also qualified from Group J.
The champions looked toothless up front, barely creating any chances of note in either half as Karim Benzema found little support in Brazilian teenage forwards Vinicius Jr. and Rodrygo.
Sociedad had already won the first leg 2-1 and cemented their spot in the decider when striker Mikel Oyarzabal scored a 41st-minute penalty after a handball in the area by a Mirandes player.
Barca were beaten 1-0 by Bilbao at San Mames, where Inaki Williams headed in a dramatic 93rd-minute winner, after La Real had seen off Madrid 4-3 in a seven-goal thriller at the Santiago Bernabeu.
The draw leaves Barca still leading with 35 points from 16 games but Real Madrid, on 34, can take their place at the top if they win at Valencia on Sunday.