In the afternoon matches, a clinical Lazio cruised to a 3-0 victory over Chievo Verona, with all its goals coming in the first half.
Antonio Candreva got the home side off to the perfect start when his effort was deflected past Chievo goalkeeper Christian Puggioni in the eighth minute following a counter.
Lazio doubled its lead against the run of play in the 38th minute. Puggioni flapped at Cristian Ledesma's cross and Luis Pedro Cavanda volleyed it in from a tight angle for his first Serie A goal.
Senad Lulic all but sealed the result three minutes later, drilling home Eddy Onazi's through ball.
Udinese captain Antonio Di Natale snatched a point for his side as a late goal on his 300th appearance for the club secured a 1-1 draw against Bologna.
Alessandro Diamanti had given Bologna the lead in the 71st minute with a stunning free kick into the top corner but Di Natale volleyed home Luis Muriel's pass five minutes from time.
Genoa picked up its first points of the season with a 3-0 win at city rival Sampdoria in the Derby della Lanterna on Sunday night.
There had been a bizarre buildup to the match with Sampdoria catching a Genoa youth team coach in full camouflage gear hiding in the bushes to spy on a training session.
Luca Antonini was making his debut after signing from Milan and he got his Genoa career off to the perfect start by volleying home Davide Biondini's cross from 15 yards in the ninth minute. It was the defender's fifth goal in 149 Serie A appearances.
Emanuele Calaio also scored on his debut, doubling Genoa's lead five minutes after halftime when he fired in Sime Vrsaljko's cross. It was another new signing who sealed the points as Francesco Lodi curled one of his trademark free kicks into the top left corner in the 66th minute.
Sassuolo remains pointless after wasting an astonishing number of chances in a 2-0 loss at fellow promoted side Hellas Verona.
Raphael Martinho and Romulo scored for Verona, which beat AC Milan on the opening day of the season.
The other promoted side, Livorno, beat Catania 2-0 with a second-half brace from Paulinho. Catania is also still to pick up a point.
