"I was happy to get that one out of the road," United manager Alex Ferguson told reporters. "The first goal was the key to it. After that they relaxed and enjoyed themselves and played very well."
Dutch midfielder Mark van Bommel claimed two goals to inspire PSV Eindhoven to a 5-0 rout of 1991 European champions Red Star Belgrade and a 7-3 aggregate win.
Bayer Leverkusen, 2002 Champions League runners-up, lost 2-1 at Banik Ostrava but advanced comfortably following their 5-0 victory two weeks ago in Germany.
Ukrainian clubs Dinamo Kiev and Shakhtar Donetsk both progressed. Kiev beat Trabzonspor 2-0 in Turkey to advance 3-2 on aggregate, while Shakhtar drew 2-2 with Club Bruges to seal a 6-3 overall victory.
Israel's Maccabi Tel Aviv eased through 4-0 on aggregate with a 1-0 home win over Greek side PAOK Salonika, and Sparta Prague beat Hungary's Ferencvaros 2-0 to advance 2-1 on aggregate.
Rangers were held to a 1-1 draw in Glasgow by CSKA Moscow, Vagner Love's 62nd-minute goal putting the Russian champions through 3-2 on aggregate.
Inter Milan, Monaco, Liverpool, Deportivo Coruna, Rosenborg Trondheim and Anderlecht reached the group phase on Tuesday.
The 16 third qualifying round winners join the 16 teams who qualified automatically.
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