Harder, who will leave the German side at the end of the season, was the first name on the score sheet after 16 minutes before netting her fourth on the 72 minute mark.
In the other quarter-final on Friday, with all four ties being played behind closed doors in Spain in rescheduled competition due to the coronavirus pandemic, France’s Kheira Hamraoui claimed the match-winner to clinch a last four spot for last year’s runners-up Barcelona in a 1-0 win over Atletico Madrid.
Barca will face Wolfsburg in Tuesday’s semi with holders Lyon facing Bayern Munich and Paris Saint-Germain playing Arsenal on Saturday for the other two berths.
Wolfsburg’s impressive display started with Harder’s effort just after a quarter of an hour before Norway’s Ingrid Syrstad Engen bagged a double, Pauline Bremer also netted before two Leanne Ross own-goals in the last 10 minutes.
Northern Ireland’s Lauren Wade’s goal after 63 minutes was the consolation for the Scottish outfit in their first appearance at this stage of the tournament.
In Bilbao, Atletico had the best of the first-half chances as left-back Kylie Strom skimmed a half-volley over the bar from close range after 11 minutes.
Hamraoui broke the deadlock with 10 minutes to play as she hit her effort into the bottom corner after a miscued pass from team-mate Asisat Oshoala.
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