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.
Manchester City's Jo Alves celebrates after scoring against Salzburg
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