AS Roma overtake city rivals Lazio to move into fourth place in Serie A.
Stephen El Shaarawy scored one goal and set up another as Roma enjoyed its seventh successive league win. It was El Shaarawy's fifth goal in six matches for Roma.
El Shaarawy signed for the Serie A club in midweek after French league side Monaco opted not to buy the striker outright.
El-Shaarawy, who has started the new campaign warming the substitutes' bench, suffered the injury in training on Friday.
El Shaarawy was the Rossoneri's top scorer in the first half of last season but hit a dry patch following the signing of Mario Balotelli.
Italy striker Mario Balotelli and German forward Marco Reus hit two goals each as their respective national side beat Malta and Kazakhstan.
Shaarawy has scored 15 goals in 22 Serie A appearances this season, and has been linked with a move to a host of other top European clubs.
Juve coach Antonio Conte said that the win was the perfect response to the weekend's shock 2-1 loss to Sampdoria in Serie A.
Arsenal manager Arsene Wenger has revealed his interest in AC Milan striker Stephan El Shaarawy, saying the Italian's "philosophy fits perfectly with mine".
Italy head coach Cesare Prandelli admitted that he had been "pleasantly surprised" by Stephan El Shaarawy and Fiorentina.