Inter Milan, considered among the Serie A title challengers this season, lost further ground by letting a two-goal led slip to draw 2-2 with Torino on Sunday meaning Luciano Spalletti's side have taken a single point from their first two games.
Champions Juventus beat Lazio 2-0 and last season's runners-up Napoli came from two goals down to rally past AC Milan 3-2 on Saturday to both start their campaigns with the maximum six points.
Inter Milan -- who returned to the Champions League after finishing fourth in Serie A last season -- had fallen to a shock 1-0 opening defeat to Sassuolo.
The northerners looked in control in the San Siro with their Argentine top scorer last season Mauro Icardi setting up Croatian World Cup finalist Ivan Perisic for the opener after six minutes with Stefan de Vrij heading the second after 32 minutes.
But Spalletti's side lost their way after an hour with Andrea Belotti pulling one back for Torino after a goalkeeping error by Samir Handanovic. New French signing Soualiho Metie earned the point on 68 minutes.
Salvatore Sirigu denied Perisic late on to give Torino their first point after last week's 1-0 loss to Roma.
Inter now trail Juventus and Napoli by five points while Roma, third last season, will bid for their second win on Monday against Atalanta.
"It's difficult to explain how we conceded those goals, but the reality is that the team is struggling with pressure," said Spalletti.
Meanwhile, surprise package SPAL, playing their second season in the top flight, are also riding high after their second win, a 1-0 victory over promoted Parma.
A Mirco Antenucci volley four minutes after the break gave SPAL all the points against the former two-time UEFA Cup winners, who are back in the top flight after three consecutive promotions saw them climb back through the divisions when bankruptcy led to automatic relegation to Serie D.
- 'Genoa in the heart' -
Meanwhile, Genoa beat Empoli 2-1 amid scenes of high emotion in their first match since the bridge tragedy in the city which killed 43 people two weeks ago.
Supporters observed 43 minutes of silence in memory of the victims whose names were flashed up on large screens in the stadium as the crowd applauded at the 43-minute mark.
"Today we were heavy in the head and in the legs, but it didn't stop us from playing a good game against a great, well-organised team," said Genoa coach Davide Ballardini.
Before all Italian top-flight games players wore T-shirts that read "Genoa nel cuore" — "Genoa in the heart" — with a design featuring a heart in the middle of the bridge.
Sampdoria, Genoa's other club, were beaten 1-0 at Udinese in their opener, after their first match had also been postponed.
Fiorentina crushed Chievo 6-1 with Giovanni Simeone scoring the final goal three minutes into injury time with his father, Atletico Madrid coach Diego Simeone, watching from the stands.