On Saturday champions Inter Milan beat Fiorentina 3-2 and AS Roma won 2-0 against Livorno.
The matches ended the long wait for the start of Italy's top flight, which had been delayed by two weeks because of the legal wrangling surrounding the match-fixing scandal.
Inter, who were fielding new signings Patrick Vieira, Zlatan Ibrahimovic and Hernan Crespo, gave a typically uneven performance at Florence's Stadio Franchi, dominating the early stages of the contest before almost allowing victory to slip from their grasp late on.
It took just 11 minutes for them to cut a swathe through Fiorentina's defence -- a rapid sequence of passes ending with Ibrahimovic cutting the ball back for midfielder Esteban Cambiasso to angle a shot past home keeper Sebastien Frey.
The Argentine international scored Inter's second goal too, a straightforward tap-in at the far post from Luis Figo's cross, before setting up Ibrahimovic for the third just after the hour.
Having dominated for the first hour Inter suddenly made a series of defensive lapses that almost cost them the match.
In the 68th minute Fiorentina's Adrian Mutu burst down the left and crossed for strike partner Luca Toni to head past visiting keeper Francesco Toldo.
Another goal by Toni -- who finished top scorer in Serie A last season with 31 goals -- ensured a nervy final few minutes for Inter.
Roma had a much easier time beating Livorno earlier in the day at the Olympic Stadium.
Their captain Francesco Totti missed a penalty, but the team cruised to victory thanks to a goal in each half by midfielder Daniele De Rossi and winger Mancini.