(CNN) -- Stuttgart survived a scare against Norwegian minnows Molde in the Europa League qualifiers, but Liverpool breezed into the next round.
The German side were 3-2 up from the first leg but struggled on home soil, going two goals down after Emil Johansson and Knut Olav Rindaroy scored.
Pavel Pogrebniak pulled a goal back for Stuttgart on 54 minutes before Timo Gebhart made sure of a 5-4 aggregate win with an injury time strike.
Liverpool had no such problems as they despatched Macedonian side Rabotnicki Kometal 2-0 to hand new coach Roy Hodgson a winning debut at Anfield.
Leading 2-0 from the first leg Liverpool repeated the scoreline. Striker David Ngog added to his two goals from the first match on 22 minutes as he headed home Joe Cole's cross from the left.
Captain Steven Gerrard then converted from the penalty spot just before halftime as Ngog was brought down in the area.
Gerrard was taken off after an hour but new signing Joe Cole completed 90 minutes on his debut for the club.
Liverpool must now negotiate another qualifying round before they can claim a place in the group stages of the competition.
Italian giants Juventus beat Irish side Shamrock Rovers 1-0 to complete a 3-0 aggregate victory.
Alessandro Del Piero scored the only goal of the game in Turin with a trademark free kick on 74 minutes.
Turkish team Galatsaray thumped OFK Belgrade, from Serbia, 5-1 to record a 7-3 aggregate victory. Australian striker Harry Kewell grabbed two goals.
Galatsaray's rivals Besiktas are safely through after they beat Czech side Plzen 4-1 on aggregate.
Portuguese side Sporting Lisbon went through against FC Nordsjælland after a 2-1 victory on home soil.
Montpelier, who finished fifth in the French League last season, were dumped out of the competition on penalties by Hungarian side Gyor.
Maccabi Tel-Aviv knocked Greek side Olympiakos out of the competition after winning their tie on away goals. Roberto Damian Colautti scored the vital goal.
Dutch team AZ Alkmaar progressed to the next stage despite losing 1-0 to Swedish side IFK Gotherborg.