Driving again for new team Hilmer Motorsport, which has taken the spot vacated by Ocean Racing Technology, free agent Dillmann produced a benchmark lap of 1m24.400s in the morning session.
That put him just 0.018 seconds ahead of Rapax's Stefano Coletti, followed by James Calado, Fabio Leimer and Felipe Nasr.
Best of the GP2 rookies was Kevin Giovesi. The Italian Formula 3 graduate, who has yet to secure a 2013 seat, was ninth ahead of his Lazarus team's confirmed driver Rene Binder.
Dillmann was second in the afternoon, 0.3s shy of pacesetter Stephane Richelmi, now at DAMS.
Formula Renault 3.5 champion Robin Frijns put Trident fifth, just behind Johnny Cecotto and Daniel Abt.
The morning featured plenty of incidents and red flags. Marcus Ericsson, Nathanael Berthon and Nasr all went off, while Adrian Quaife-Hobbs and Abt had a coming together.
There were fewer interruptions in the afternoon, which ran smoothly bar a late stoppage after a mistake at the first corner by Coletti.
- Sports & Recreation
- Stefano Coletti
- James Calado
- Felipe Nasr
- Ocean Racing Technology
- Fabio Leimer