Juventus were held to an uneventful goalless draw by Sampdoria on Monday (Aug 22), while Chris Smalling headed Roma to a 1-0 win over Cremonese to make it two wins from two.
Massimiliano Allegri's side were uninspired and failed to create much against a solid Samp at the Stadio Luigi Ferraris in Genoa.
The closest they came to taking the points was when Adrien Rabiot's low strike was correctly ruled out for offside, the France midfielder a starter after his move to Manchester United collapsed in the week.
Filip Kostic also forced a save from Emil Audero in stoppage time but that was about it from a team aiming to make a league title charge after finishing way behind champions AC Milan last term.
"The positive thing is that we haven't conceded in two games," Allegri told DAZN.
"In the second half we did some good things, we scored a goal and created a great chance at the end... but we've left two points behind here."
Juve were missing the injured Angel Di Maria and they lacked the stardust which the Argentina winger brought to the team in their season-opener win over Sassuolo last week.
Their sole decent opportunity in the first half was created by a bursting run in the 15th minute from Juan Cuadrado, who however after robbing Tommaso Augello could only shoot straight at Emil Audero in the Samp goal with Dusan Vlahovic to his right.
Vlahovic barely had a touch in the first 45 minutes beyond kicking the ball onto his own post at a corner and was livid with the Colombian for not passing.
The Serb started the second period brighter however, flashing a shot wide and claiming in vain for a penalty when clashing with the excellent Omar Colley.
He thought he had set up Juve's opener when Rabiot met his pass with a perfect low finish, but after awarding the goal referee Rosario Abisso then ruled the goal out for Vlahovic straying offside following after a VAR check.
Substitute Fabio Quagliarella almost made it a fairytale ending for Samp when he flashed a snap shot wide with a minute left on the clock, but Audero kept out Kostic's scuffed volley and both sides had to settle for a point.
Smalling saves Roma
Chris Smalling scored the winning goal as Jose Mourinho's Roma edged past promoted Cremonese to make it two wins from two in Serie A this season. The Englishman headed in at the back post in the second half from Lorenzo Pellegrini's corner.
Cremonese's best chance fell to striker Cyriel Dessers, but the Nigerian's strike rattled the crossbar.
Roma, who won the inaugural Europa Conference League last season, are yet to concede this campaign.
