In his first meeting with Roma since his sacking two years ago, Zeman watched his new team concede two decisive goals in the opening 13 minutes.
Mattia Destro converted the first from close range following neat build-up, before Alessandro Florenzi doubled the hosts' advantage three minutes later.
Roma's bid to continue their 100 per cent start to the season went unthreatened from then on, but it wasn't all good news as Daniele De Rossi was withdrawn due to injury in the closing stages.
Elsewhere, Inter's strong start stuttered in Sicily as they were held to a 1-1 draw by Palermo.
Hellas Verona jumped to second spot with a 1-0 win at Torino courtesy of Artur Ionita's 66th-minute winner, making it back-to-back wins for Andrea Mandorlini's men.
The hosts found themselves under pressure for long periods, but Stefano Pioli's men were disrupted by injuries to Lucas Biglia, Dusan Basta and Santiago Gentiletti before Stefan de Vrij's 85th-minute sending off swung the game in Genoa's favour.
There was yet more disappointment for Rafael Benitez on Sunday as Danilo's sliding finish at the back post from Antonio Di Natale's clipped free-kick helped Udinese defeat Napoli 1-0 at home.
And in Veronia, three quick goals in 10 minutes helped Parma claim their first win, as they defeated Chievo 3-2.
Mariano Izco gave the hosts the lead but Antonio Cassano scored twice, either side of Massimo Coda's half-volley, to give Parma a two-goal cushion with 15 minutes to play.
