Last season's finalists Juventus remain second in the group following the stalemate, a point ahead of third-place Sporting Lisbon, and can secure their qualification with victory at Olympiakos on December 5.
Five-time European champions Barca came into the clash needing just a point to finish first in Group D, while Juventus needed to avoid defeat and Sporting to fail to beat Olympiakos in Lisbon in order to qualify.
But the Portuguese beat their Greek rivals 3-1 in Lisbon, leaving Juve needing three points in Athens to be sure of a last-16 place.
Messi came on after 56 minutes but could not follow up on the brace he scored in the 3-0 beating Barca inflicted on Juve at the Camp Nou in September.
Juventus boss Massimiliano Allegri recalled veteran duo Gianluigi Buffon and Andrea Barzagli after they were left out for Sunday's 3-2 defeat at Sampdoria following Italy's failure to qualify for the World Cup.
In a first half lacking the quality expected of such a high-profile fixture, Brazilian Douglas Costa demonstrated early pace, forcing a save from Marc-Andre ter Stegen after two minutes at the Allianz Stadium.
Croatian midfielder Ivan Rakitic went closest for Barca after 22 minutes, when his free-kick struck the post after making its way through a crowded box.
Dybala looked like he was set to break through just before half-time when he picked up an Alex Sandro cross to go on a mazy run, but his shot from a tight angle flew over the bar.
After the break, a Luis Suarez free-kick was deflected over the bar before Messi came on in place of Gerard Deulofeu, and the Argentina forward also fired a free-kick high over Juventus stopper Buffon.
But Dybala thought he had won it in stoppage time from a corner, only for Ter Stegen to push the shot away and guarantee his side a place in the knockout stage.
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