Gianluigi Buffon kept out Francesco Totti's second-half penalty to extend Juventus' unbeaten run in Serie A to 14 games.
Daniele De Rossi had put Roma ahead in the fifth minute before Giorgio Chiellini equalised on the hour mark.
Roma had a chance to go in front two minutes later but Totti's central spot-kick was saved by Buffon.
The Turin giants climbed back to the top of the standings with the draw and are level on 30 points with Udinese.
Roma, who went into the game at the Stadio Olimpico on the back of two straight defeats, dropped to ninth.
The hosts got off to the perfect start, Arturo Vidal failing to clear Totti's cross and De Rossi made no mistake in hitting the ball past Buffon.
Juventus almost pulled level in the 12th minute when Simone Pepe got his head behind Alessandro Matri's cross but his effort went over.
Midway through the half, Roma goalkeeper Maarten Stekelenburg kept out Marcelo Estigarribia's eight-yard shot.
The visitors continued to push forward and twice had the chance to equalise before the break. In the 38th minute, Vidal found Pepe inside the area and his strike was saved by Stekelenburg. The Roma goalkeeper then kept out Stephan Lichtsteiner's header from Andrea Pirlo's cross.
Juventus picked up where they left off after the re-start and levelled in the 61st minute when Chiellini headed Estigarribia's cross-shot past Stekelenburg.
Roma could have gone back in front one minute later after Vidal brought down Erik Lamela in the area. Totti struck the resulting spot-kick with power but right down the middle and Buffon kept it out.
Juventus then had an opportunity to take all three points with two minutes remaining when Eljero Elia found substitute Fabio Quagliarella in the box and his strike was saved by Stekelenburg.