Juventus were held to an uneventful goalless draw by Sampdoria on Monday, 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
England defender Smalling met Lorenzo Pellegrini's corner in the 65th minute with a perfect header to send a wave of relief around a packed Stadio Olimpico and secure a hard-fought win.
The 32-year-old dedicated his winner to Wijnaldum, who signed from Paris Saint-Germain earlier this month but fractured his shin in training on Sunday.
"We're gutted for him and we hope he's back as soon as possible because he's such a quality addition for us," Smalling told DAZN.
Roma, who travel to Juve on Saturday, have a maximum six points from their first two games after a summer full of optimism following their Europa Conference League triumph last season and an impressive transfer window which also brought in Paulo Dybala.
Already reeling from Wijnaldum's injury, more of that positive feeling was drained when starlet Nicolo Zaniolo had to be taken from the field just before halftime with a left shoulder injury following a thumping tackle from Luka Lochoshvili.
Fans were anxious after the exit of the 23-year-old Italy international, who has already suffered serious injuries to both his knees in his short career, but he later said on Instagram he would be back "in three weeks".
Without him, Roma had one less threat against Massimiliano Alvini's stubborn Cremonese, who might be on zero points but will trouble a lot of teams in Serie A if they put in more bold displays like Monday's.
Twice Cyriel Dessers went close with bicycle kicks and just after the break smashed a superb half-volley against the crossbar.
Charles Pickel then nearly snatched a point for Cremonese in stoppage time when his rocket shot fizzed millimetres wide.
But Smalling's header across Ionut Radu was just enough to gain the three points and join Inter Milan and Napoli at the top of the table.