Europa holders Atletico lose to Aris
Manchester City won 2-0 at Salzburg in a clash of two big-spending clubs who had been aiming for the Champions League but had to settle for the second-tier competition.
None of Italy's four representatives won a game between them while three of the four Spanish teams were beaten.
Juve's Brazil World Cup villain Felipe Melo gave away an early penalty as the Italians fell two goals behind with Artjoms Rudnevs grabbing a hat-trick for the visitors including a stoppage-time equaliser in their Group A match.
Felipe Melo, who enhanced his reputation for reckless tackling by getting sent off in Brazil's World Cup quarter-final defeat by Netherlands, produced a familiarly clumsy challenge in the 13th minute and Rudnevs opened his account from ths spot.
The Latvian was on target again on the half hour, snapping up a rebound, but Juve equalised when defender Giorgio Chiellini scored either side of halftime before Alessandro del Piero put them ahead in the 68th minute with a superb left-foot strike.
However, the Poles left Italy with a point when Rudnevs equalised in the second minute of added time.
Aris's Spanish forward Javito scored just before the hour against Atletico in Group B, running onto a flicked pass by Carlos Ruiz and firing a powerful shot into the corner, as they preserved an unbeaten home record in European competition.
Spain forward David Silva and Brazilian striker Jo scored in each half to give the world's richest club Manchester City a 2-0 win at wealthy Austrian champions Salzburg in Group A.
City failed to make the Premier League top four last season while Salzburg, bought by the Red Bull soft drinks company in 2005 amid protests by fans, have lost in the Champions League qualifying rounds four times in the last five seasons.
Liverpool cruised to a 4-1 win over Steaua Bucharest in a Group K meeting of two former European champions.
Joe Cole put the hosts ahead in the first minute only for Cristian Tanase to level 12 minutes later. Liverpool striker David Ngog scored twice in the second half, including a penalty, with Brazilian midfielder Lucas notching the other goal.
Aleksandr Kerzhakov hit a first-half hat-trick as 2008 UEFA Cup winners Zenit St Petersburg won 3-1 at Anderlecht in Group G.
Patrick Helmes also scored a treble to help Bayer Leverkusen, missing injured captain Michael Ballack, a 4-0 win over Rosenborg