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100 per cent start to the season went unthreatened from then on, but it wasn't all good news as Daniele De Rossi was withdrawn due to injury in the closing stages.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.
An early error from Nemanja Vidic gifted Franco Vazquez the opener before Mateo Kovacic came up with a fine 20-yard drive to level before half-time.
Inter had two goals chalked off either side of the break before Palermo struck the bar and had a goal of their own disallowed in the 88th minute in a thrilling end to the contest.
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.
And Genoa snatched a dramatic first success of the season as substitute Mauricio Pinilla scored a diving header in the 87th minute at home against Lazio.
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.
Alberto Paloschi scrambled the ball over the line from a corner to set up a nervous finish but the visitors held on.
Fiorentina fought to their first win of the season, away at previously unbeaten Atalanta, Jasmin Kurtic settling it with a driven left-foot shot across the keeper from 18 yards.
Meanwhile, struggling Sassuolo survived the visit of Sampdoria without the suspended Domenico Berardi as their match finished goalless.
