The Chilean midfielder struck with two penalties in the 29th and 60th minutes and added a brilliant looping header to put Antonio Conte's side into second place in Group B on six points, seven behind leaders Real Madrid but two ahead of Galatasaray and Copenhagen.
Olof Mellberg equalised for the Danish champions in the 56th minute with a smart volleyed finish after a long throw caused confusion in the hosts' defence.
Juve now need only a draw in Istanbul in the final round of group games to qualify from the group despite coming into Wednesday's game with only three points from their four previous matches.
(Reporting by Terry Daley, editing by Stephen Wood)
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