The England international, who linked up with Jose Mourinho when he made a £34million switch from Chelsea earlier this month, scored Roma's third goal with a fine finish after Lorenzo Pellegrini and Jordan Veretout had put them in control.
Pellegrini's second goal of the game wrapped up a routine win.
Another former Chelsea striker, Olivier Giroud, scored twice for AC Milan as they claimed a convincing 4-1 victory over Cagliari, Napoli won 2-1 at Genoa and Sassuolo played out a goalless draw with Sampdoria.
Barcelona handed teenager Gavi his competitive debut in their 2-1 win against Getafe.
The 17-year-old midfielder impressed as first-half goals from Sergi Roberto and Memphis Depay ensured Barca made it two wins from two at the Nou Camp this season.
Rayo Vallecano had four different goalscorers - Alvaro Garcia, Oscar Trejo, Randy Nteka and Santi Comesana - in a 4-0 thrashing of Granada, who have yet to win a LaLiga game this season.
And stoppage-time goals from Roberto Torres - a penalty - and David Garcia stunned Cadiz as Osasuna snatched a 3-2 win.
Lionel Messi had to settle for a substitute appearance as Kylian Mbappe stole the headlines with both goals in Paris St Germain's 2-0 win at Reims.
Entering the action in the 66th minute to replace Neymar, the Argentinian's first touch was greeted with screams and cheers from the 6,000 travelling fans.
But it was reported Real Madrid target Mbappe who stole the show, opening the scoring after 15 minutes and wrapping up the points just after the hour.
Elsewhere in Ligue 1, last season's title winners Lille beat 10-man Montpellier 2-1.
Yusuf Yazici had opened the scoring for Lille in stoppage time at the end of the first half, but there was still enough time for Gaetan Laborde to equalise before the half-time whistle.
Jonathan David scored the winner before Montpellier's Junior Sambia was shown a straight red card with just over 15 minutes remaining.
A goalkeeping howler from Rennes' Alfred Gomis gifted Angers' their opening goal in a 2-0 win that moved them third, while Clermont drew 2-2 with Metz and Lens played out the same result against Lorient.
Strasbourg beat Brest 3-1 and Sofiane Diop scored twice as Monaco won 2-1 at Troyes.
In the Bundesliga, table-topping Wolfsburg maintained their perfect start to the season with a narrow 1-0 win over RB Leipzig.
Jerome Roussillon scored the only goal of the game just after half-time. Union Berlin also secured a 2-1 win over Borussia Monchengladbach.