The two, separated at the top by 14 points after eight races, got back down to business after calming a 'road rage' controversy that has dominated Formula One since the previous race in Azerbaijan last month.
Hamilton, the only driver on the current grid to have won in Austria following the retirement of 2016 champion and team mate Nico Rosberg, swiftly demolished the lap record he set last year.
The Briton then lowered his morning time by another half second in the afternoon to end the day with a best time of one minute 05.483 seconds.
In changeable conditions in the scenic Styrian hills, with bright sunshine mixed in with the occasional rain shower, four times world champion Vettel was second on the timesheets with a lap 0.147 slower than Hamilton's.
Red Bull's Dutch teenager Max Verstappen had been second in the morning, when Vettel was only fourth and half a second off the pace.
Mercedes have won every year since Austria returned to the calendar in 2014, after being absent for a decade, with Hamilton triumphant in 2016.
The Briton and his Ferrari rival have been closely matched on race pace, with each winning three grands prix so far this season.
Vettel will be happy to have the focus back on the racing after making a public apology to Hamilton for the Baku furore last month and his comments afterwards.
The German had driven into the back of Hamilton's car, while the race leader was waiting for the safety car to pit, and had pulled alongside to remonstrate. He ultimately finished fourth, a place ahead of Hamilton. He then accused Hamilton of "brake-testing" him, words he retracted this week.
Hamilton's team mate Valtteri Bottas was third fastest in both sessions, with Verstappen dropping back to fourth in the afternoon after being sidelined early in the session with a brake problem.
Red Bull's Azerbaijan race winner Daniel Ricciardo and Ferrari's Kimi Raikkonen were fifth and sixth in both.
Ricciardo injected some Australian humour into the build-up when he jokingly told Sky Sports television, while struggling to keep a straight face, that Baku had changed everything.
"I always said I want to win five races and retire so I'm probably not going to compete this weekend," he smiled. "I think I'm done. So it's changed pretty dramatically my position in the sport."
He then reassured "people at home who don't understand my silly sense of humour" not to worry.
(Editing by John O'Brien and Susan Thomas)
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