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.
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.
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 attacking starlet Nicolo Zaniolo had to be taken from the field just before half-time with a left shoulder injury following a thumping tackle from Luka Lochoshvili.