The former Liverpool and Chelsea manager has been tasked with beating Juventus to the Scudetto and his side fired an early warning shot to the reigning champions.
Summer signing Jose Callejon scored a debut goal after dazzling with his skills in the first half and fan favourite Marek Hamsik made sure of the points with goals either side of half-time.
Napoli's former boss, Walter Mazzarri, claimed victory in his first league game as Inter Milan coach but the manner of an uninspiring 2-0 win over Genoa left him with plenty to think about.
Inter, who finished a dismal ninth last season, toiled without reward for 75 minutes against Genoa until Yuto Nagatomo's fortuitous finish sparked a late rally.
Rodrigo Palacio's goal in second-half stoppage time flattered Inter as Genoa, who narrowly avoided relegation in May, had looked a much-improved side across 90 minutes.
Rudi Garcia's career as Roma coach began with a convincing 2-0 win at newly promoted Livorno.
The French tactician, who left Lille in the summer, watched existing Giallorossi regulars secure all three points at the Stadio Armando Picchi as Alessandro Florenzi followed up Daniele De Rossi's half-volleyed thunderbolt.
It was a third league goal against the Tuscans for Italy midfielder De Rossi, as he brought his 25-game domestic goalscoring drought to an end to kickstart Roma's season.
Early goals from Hernanes and Antonio Candreva were enough for Lazio to secure a 2-1 win over Udinese.
Substitute Luis Muriel pulled a goal back for Udinese on the hour but the Biancocelesti held on for a deserved win.
Lazio fans were barred from entering the north stand of the Stadio Olimpico as punishment after a section of supporters directed racist abuse at Juventus players in last weekend's Supercoppa Italiana.
Matias Cabrera's goal just after the hour mark ensured Cagliari began their campaign in the right manner after they came from behind to see off Atalanta 2-1.
Cabrera fired home from close range in the 63rd minute to guarantee the three points for the Sardinians at Trieste's Stadio Nereo Rocco.
The away side had taken a 27th-minute lead through Guglielmo Stendardo, but Cagliari hit back less than 60 seconds later through Radja Nainggolan before their comeback was completed by Cabrera.
Sassuolo's first foray into Serie A football ended in a 2-0 defeat to Torino as the newcomers paid the price for some poor finishing at the Stadio Olimpico.
The Serie B champions gave a good account of themselves in their season opener, but their failure to find the target cost them dearly as they succumbed to goals from Matteo Brighi and Alessio Cerci.
Elsewhere, Parma were denied a win at the start of their centenary season as Chievo rode out a goalless draw at the Stadio Ennio Tardini.
On Saturday, Carlos Tevez marked his Serie A debut with the winning goal for Juventus as the champions began their bid to win a third straight Scudetto with a 1-0 victory at Sampdoria.
The former Manchester City striker, a marquee signing for Antonio Conte's team this summer, has scored fancier goals than the close-range finish that earned all three points in Genoa.
He has scored many more important in his time with Boca Juniors, Corinthians, West Ham, Manchester United and City, and the Argentina national team.
But there was no faulting Tevez's timing, or his form, as he made the difference in Serie A's big opening Saturday night game.
Verona came from behind to score a shock 2-1 win over AC Milan in the first game of the season.
It looked like being business as usual when Andrea Poli gave the Rossoneri a 14th-minute lead following good work from Mario Balotelli.
But two Luca Toni headers, one either side of half-time, turned the game around and allowed Verona at least a couple of hours as league leaders.
Saturday's Serie A Results
Sunday's Serie A Results
Monday's Serie A Fixture