Antonio Conte's men failed to win any of their first four games in Europe's premier club competition and sit bottom of Group B with three points.
However, thanks mainly to the dominance of runaway pool leaders Real Madrid - who have taken 10 points from their four games, scoring 14 goals in the process - Juve are still just one point behind Galatasaray and Copenhagen.
That means the Italian champions could end matchday five in control of their own destiny in terms of reaching the last 16, as a home victory over the Danes - coupled with a defeat for Galatasaray at Santiago Bernabeu - would put them second with just one game remaining.
Conte's side are sure to head into the crucial fixture high on confidence after they moved to the summit of Serie A by recording their fifth straight league win with a 2-0 success at Livorno on Sunday.
Fernando Llorente continued his rich vein of form by opening the scoring with his third goal in as many games at club level, before the Spaniard set up strike partner Carlos Tevez to end a run of three matches without scoring to seal the points.
Juve have not won in their last three home Champions League games, but are unbeaten in 12 in all competitions on their own patch, a run stretching back to last season's quarter-final defeat by Bayern Munich.
Copenhagen, meanwhile, head to Turin buoyed by their 1-0 victory over Galatasaray on matchday four.
Stale Solbakken's team have not lost in six games in all competitions and comprehensively overcame Viborg 4-1 in their last Superliga fixture on Sunday, with forward Igor Vetokele scoring twice to take his tally to seven for the season.
Juve needed a second-half equaliser from Fabio Quagliarella to take a point from the reverse match at Parken in September, but the Danish champions have conceded seven goals in their away games at Real and Galatasaray this term.
MasterCard is excited to present episode three of the Priceless Memories UEFA Champions League video series. See what Manchester United legend Andrew Cole had to say!