Former European champions Liverpool and Juventus progressed to the last 16 and Werder Bremen striker Claudio Pizarro scored a hat-trick as his side went through with a 4-1 win over former England manager Steve McLaren's Twente Enschede.
Sixteen-year-old Romelu Lukaku set Anderlecht on the way to a 4-0 win over Athletic Bilbao, one of two Spanish sides to suffer a heavy defeat as Villarreal lost 4-1 at VfL Wolfsburg.
However, Diego Forlan's 90th-minute goal gave Atletico Madrid a 2-1 victory at Galatasary to send them through 3-2 on aggregate and Valencia beat Club Bruges 3-0 for a 3-1 aggregate win.
Eight teams had dropped into the competition in this round after failing to qualify in the Champions League and seven went through - Liverpool, Atletico Madrid, Juventus, Rubin Kazan, VfL Wolfsburg, Standard Liege and Olympique Marseille.
Romanian side Unirea Urziceni were the exception as they lost 3-1 at home to five-times European champions Liverpool.
Shakhtar coach Mircea Lucescu, whose team were 2-1 behind from the first leg, had billed their tie with Fulham as a duel between his side's "spectacular and skilful" football and what he described as the English team's more physical approach.
The Ukrainians, who won the final UEFA Cup last season before it was rebranded as the Europa League, had 14 shots to Fulham's two in the first half but it was the visitors who went ahead with a Brede Hangeland header.
Jadson, one of five Brazilians in the Shakhtar side, swept in the equaliser in the 69th minute but Fulham held on for a 3-2 aggregate win to set up a last 16 tie with Juventus.
Three-times UEFA Cup winners Liverpool won at Unirea despite going behind to a Bruno Fernandes header.
Argentina midfielder Javier Mascherano levelled with a 25-yard drive before Dutch winger Ryan Babel put the visitors ahead with a sharp turn and shot four minutes before halftime.
Captain Steven Gerrard completed a 4-1 aggregate victory just before the hour for Liverpool, who now play French side Lille after they drew 1-1 at Fenerbahce for a 3-2 win overall.
BARE MINIMUM
Juventus did the bare minimum to knock out Ajax Amsterdam, a goalless draw at home sending them through 2-1 on aggregate in a tie between two teams who twice met in the European Cup final.
German clubs scored a double over Dutch rivals as Werder Bremen's success over Twente was matched by Hamburg SV who eliminated PSV Eindhoven.
Peru striker Pizarro scored twice in a five-minute first-half spell for Werder and completed his hat-trick just before the hour. Brazilian defender Naldo notched the other goal in a 4-2 aggregate win.
Hamburg SV lost 3-2 on Thursday but went through on away goals after a 3-3 aggregate draw against PSV on an eventful night for the Dutch team's Balasz Dzsudzsak, who scored and was later sent off for pushing the referee.
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