Liverpool and Juventus had no such problems as they strolled to home wins over Rabotnicki and Shamrock Rovers respectively in their third qualifying round, second leg ties.
Trailing 3-2 from their home leg, Molde scored either side of half-time to stun Christian Gross' team, who last season reached the last 16 of the Champions League.
Emil Johansson fired Molde ahead four minutes before the break and Knut Rindaroy added a second shortly after the restart.
But Russian striker Pavel Pogrebnyak headed one back from a free-kick and Timo Gebhart headed a stoppage time equaliser to give the Bundesliga side a 2-2 draw and 5-4 aggregate win.
David Ngog, who scored both goals in Liverpool's 2-0 first leg win last week against their Macedonian opponents, wrapped matters up when he headed Liverpool ahead after 22 minutes after a perfect pass from Joe Cole, making his competitive debut.
The five-time European champions doubled their lead after 40 minutes when Steven Gerrard scored from the spot after Fernando Lopes hauled down Ngog to complete a 2-0 win and go through 4-0 on aggregate.
Alessandro del Piero's 74th minute goal gave Juventus a 1-0 win at home to Shamrock Rovers as they won 3-0 on aggregate.
Australian Harry Kewell scored twice, including one penalty, to help Galatasaray demolish OFK Belgrade 5-1 away and win 7-3 on aggregate, after they had been held at home in the first leg.
Olympiakos were knocked out, losing 1-0 at Maccabi Tel Aviv where Roberto Colautti scored a 42nd minute goal to send his side through on away goals after a 2-2 aggregate draw.
Fellow Israelis Maccabi Haifa, who took part in the Champions League group stage last season, were on the wrong end of an upset against Dynamo Minsk.
The Belarus team came from behind to win 3-1 and go through 3-2 on aggregate.
Azerbaijan's Qarabag - knocked out at the play-off stage last year by Twente Enschede - also went into the next stage as a 3-2 win over 12-times Polish champions Wisla Krakow gave them a 4-2 aggregate win.
Sibir Novosibirsk, the most easterly club to have taken part in European competition, went through despite a 2-1 defeat at Apollon.
Jose Semedo and Antonio Nunez scored for the Cypriots but Igor Shevchenko's 63rd minute goal was enough to take the Russians through on away goals after a 2-2 aggregate draw.
Former European champions Red Star Belgrade were also knocked out after a 1-1 draw at Slovan Bratislava, the Slovak side winning 3-2 on aggregate.
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