Benfica also made a winning start in their first leg tie, beating Anderlecht 1-0 in Lisbon to stake their claim to a place in the lucrative group phase after the second-leg games in two weeks' time.
The upset of the night came in Turin, where Andreas Johansson converted a penalty for the unfancied Swedes in first-half stoppage time and Tobias Hysen made it 2-0 just four minutes after the re-start.
Juventus hit back with goals from France striker David Trezeguet and new Brazilian midfield signing Emerson within 10 minutes, but still left themselves on the losing end of the away goals rule in coach Fabio Capello's first competitive game in charge.
Finalists in 2003, Juventus will still be fancied to qualify for the group phase after a game which their influential Czech playmaker Pavel Nedved missed through injury.
Captain Steven Gerrard scored both goals in a Liverpool victory which added to speculation that England striker Michael Owen might be leaving the premier league club.
Owen, who was linked with a move to Real Madrid by British media reports on Tuesday, was kept on the substitutes' bench -- thereby avoiding an appearance that would have left him cup-tied in Europe for any club wishing to sign him this season.
The speculation did not dampen a convincing performance in Liverpool's first competitive game under new boss Rafael Benitez.
Gerrard, who was only denied a hat-trick by a disallowed goal, rifled home a superb first-time shot from 20 metres after 23 minutes and followed up with an angled drive from inside the box in the 79th minute.
Slovenian midfielder Zlatko Zahovic got Benfica's winner against an Anderlecht side who failed to take their chances.
Trabzonspor came from a goal down to win 2-1 at Dynamo Kiev, Maccabi Tel Aviv beat PAOK Salonika by the same score in Greece and CSKA Moscow will take a 2-1 lead over Rangers to Glasgow after Czech midfielder Jiri Jarosik hit a second-half winner.
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