The Briton, who is 22 points behind the German after seven races, lapped the Red Bull Ring with a fastest time of one minute 09.542 seconds on super-soft tyres in an afternoon session that stayed dry despite dark clouds overhead.
Rosberg had been quickest on a rain-affected morning with a best effort of 1:11.295, with Hamilton 0.140 behind, but was a considerable 0.377 slower than the 2008 world champion in a windy second practice.
The two Mercedes were the only cars to lap in under one minute 10 seconds.
Hamilton has won four races to Rosberg's two so far this season, but has also suffered two costly retirements through no fault of his own.
"It didn't feel bad out there today considering this is a new track to me. Already after the first few laps I was feeling comfortable and always seemed to be finding time with new lines and improvements," said Hamilton.
"To be as quick as I was considering others have already driven this track is a great feeling. It was very windy out there today, but we got a lot of running and we feel set for the race on Sunday."
"If the car is like this for the race, I'm in a good place."
Rosberg's car needed the ERS cooling pump replaced between the sessions and he reported his car was bouncing down the straights.
"In general it was a complicated day for me, so there is still some lap time to find compared to my team mate and there is a lot of work required from me tonight," he said.
ALONSO THIRD
Ferrari's Fernando Alonso, one of just four current drivers to have raced previously at what was formerly the A1 Ring, finished third in both sessions.
Mercedes-powered Williams again looked strong, with Brazilian Felipe Massa fourth in the morning and Finnish team mate Valtteri Bottas filling that position in the afternoon.
"The car is reasonable on both new and scrubbed tyres and we are where we thought we would be in terms of pace," said the team's head of performance engineering Rob Smedley.
"It's very close from the second quickest car backwards so we are going to work hard to make sure we go through the smallest details in order to improve further."
Red Bull's four-time world champion Sebastian Vettel had a spectacular spin in the morning, but was sixth fastest after lunch, as several drivers ran wide at the fast and scenic circuit in the southern Styrian mountains.
The German, whose mechanics changed the car's floor after his high-speed spin at the exit to the last corner, was lucky not to clout the barrier at the Red Bull-owned track.
Australian team mate Daniel Ricciardo, winner of the previous race in Canada, was 13th and eighth fastest respectively amid intermittent rain and after also having his car's floor changed.
McLaren's Jenson Button was fifth and seventh in the sessions but complained that the supersoft tyres were suffering heavy wear.
Sunday's race will be the first at the renovated track, one of the shortest on the calendar, since 2003.
Pirelli expect two stops to be the norm, with warmer weather predicted for the weekend.
(Writing by Alan Baldwin, editing by Sudipto Ganguly/Pritha Sarkar)
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