Williams’ Valtteri Bottas was fourth, followed by Sauber’s Felipe Nasr, the Red Bulls of Daniil Kvyat and Daniel Ricciardo, and Toro Rosso’s Max Verstappen.
Cool conditions and a rather green track surface combined to make for plenty of off-track moments as the drivers got to grips with the challenging, 4.326-kilometre Spielberg circuit. Rosberg and Hamilton were among those to make mistakes - the Briton at Turn 8 after setting two personal best sector times, and again at Turn 1, where Rosberg later went off.
It was Rosberg who had the upper hand though, edging Hamilton by three tenths over a single lap and also on race pace when the field switched to longer runs in the final part of the session.
Vettel and Alonso, in contrast, were in trouble almost immediately. Alonso had completed just one lap when he lost power at Turn 8 and had to coast back to the pits, where his car remained until the final 15 minutes. McLaren did at least manage to cure some of Alonso’s woes, though he still only completed 10 laps.
Vettel meanwhile lost drive just over 20 minutes into the 90-minute session and despite frantic work from his Ferrari mechanics was unable to add to his tally of four laps.
Things then nearly got a whole lot worse for the Scuderia. Williams had just waved Felipe Massa out of his pit box when Ferrari boss Maurizio Arrivabene started to run from the pit wall to the garage. Fortunately, Massa saw what was happening and stopped, as the Italian jumped back out of the way...
In the end, the overall order suggested that some might have been running more fuel than others.
Kimi Raikkonen flew the flag for Ferrari to go third, 0.627s off Rosberg - a measure of encouragement for Ferrari since Vettel is usually a little faster than the Finn over a single lap. Valtteri Bottas was fourth for Williams, fractionally ahead of Sauber's Felipe Nasr and Red Bull duo Daniil Kvyat and Daniel Ricciardo, who were split by less than 0.1s.
Toro Rosso's Max Verstappen - racing on a circuit he has previous experience of for the first time in F1 - was eighth ahead of Felipe Massa in the second Williams, Force India's Sergio Perez and Carlos Sainz in the second Toro Rosso. Interestingly, Verstappen complained that his car undriveable thanks to oversteer, something with which Kvyat also struggled, but they were still respectably fast.
Lotus had great straight-line speed, but Pastor Maldonado was only 12th, two spots ahead of Jolyon Palmer, standing in for Romain Grosjean for FP1. The pair sandwiched Le Mans 24 Hours winner Nico Hulkenberg in the second Force India.
Marcus Ericsson took 15th for Sauber, as Jenson Button struggled with serious vibrations, poor ERS performance and sticky gears on his McLaren to take 16th, one spot ahead of Alonso. Will Stevens and Roberto Merhi were 18th and 19th respectively, with Vettel propping up the timesheet.
Midway through FP1, it was also officially confirmed that Ricciardo will be using a fifth engine this weekend - as will Alonso, who will also take a fifth turbocharger and MGU-H. It will mean a 10-place grid drop for the former, and a 20-place drop for the latter.