The three-time defending Serie A champions saw their hopes of reaching the last 16 of Europe's premier club competition placed in serious jeopardy during their 3-2 win over Olympiacos on Tuesday.
Juve - who had lost two of their first three Group A matches at Atletico Madrid and Olympiacos - found themselves 2-1 down just after the hour mark.
However, an own goal from Olympiacos goalkeeper Roberto and Paul Pogba's 18-yard strike saved Juventus, leaving them behind the Greek side on goal difference alone.
A second successive failure to reach the Champions League's knockout stages would be hugely disappointing for a Juve side who have enjoyed domestic dominance in recent years.
Their escape is sure to boost spirits, though, and winger Roberto Pereyra said the league leaders must keep their foot on the pedal in the coming weeks.
"I think that the game against Parma will be difficult. That's for sure," Pereyra told Juventus TV.
"But we have to keep playing like we are doing now.
"We are on the right track and we must keep playing like this if we want to remain at the top."
Juve regained their three-point lead atop Serie A with a 2-0 win at Empoli on Saturday.
Second-placed Roma lost to Napoli on the same day - starting what has been a particularly good week for Massimiliano Allegri's men.
Andrea Pirlo had not scored this term before the Empoli win, but two goals from free-kicks in as many matches are sure to have lifted the 35-year-old playmaker, who starred against Olympiacos.
Fernando Llorente also made a significant contribution off the bench in midweek and could win his starting spot back off the ineffective Alvaro Morata.
Parma sit 19th in Serie A - but did climb off the bottom with a shock 2-0 win over Inter last time out.
Roberto Donadoni's men have not drawn any of their 10 matches this season, winning two and losing eight, and only forward Antonio Cassano (five goals in nine matches) has been a consistent performer.
Parma have won just one of their last 11 away matches in Serie A, although they were only beaten 2-1 at Juve in March this year.
Kwadwo Asamoah (knee) will miss out for Juve, while defenders Andrea Barzagli and Patrice Evra are also likely to sit out with injury worries.
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