The English driver was forced to again settle for finishing as runner-up behind Rosberg as Mercedes scored a sixth one-two in eight races. Ahead of the British Grand Prix in two weeks' time, Hamilton now trails Rosberg by 29 points in the drivers' standings as the German has yet to finish out of the top two this year.
Yet Hamilton's performance was a credible one, notable for a stunning performance on lap one in which he rocketed from ninth on the grid to fourth.
Strategy then helped both men take full advantage of the pit stops as they were able to move ahead of Williams' Felipe Massa and Valtteri Bottas, who finished fourth and third respectively after starting on the front row.
For Hamilton, there was the realisation he should never have started from such a lowly position initially, a consequence of his errors in qualifying that left him without a time in the final session.
The first lap was special, though, as he scythed his way in between Ferrari's Kimi Raikkonen and Daniil Kvyat in his Toro Rosso.
After that, Hamilton took advantage of Daniel Ricciardo's mistake at the first corner, flashed by McLaren's Kevin Magnussen on the run up to turn two, before diving down the inside of Fernando Alonso in his Ferrari at turn eight of the short nine-corner Red Bull Ring.
"We've been working very hard on our starts throughout the year," said Hamilton. "Naturally, it would have been great if I'd started where perhaps I should have done this weekend - but damage limitation. To go from ninth to second and be pressuring Nico at the end of the race really shows the pace I had this weekend."
With Mercedes performing the undercut in the pit stops to get their drivers past Massa and Bottas, the final third of the race was a run to the line for Hamilton and Rosberg.
Hamilton, though, failed to get within a second at any stage of Rosberg to make any kind of move as they matched one another on pace to the chequered flag.
Notably, Hamilton lost 1.9sec to Rosberg over the course of the two stops, and that was the difference between them at the end. It is understood Hamilton was marginally out of place at the first, while at the second there was a problem with replacing one of the wheels.
Two retirements have cost Hamilton dear, so as far as Rosberg was concerned, to finish ahead of him again was crucial. "Twenty-nine points is a nice gap, but it's still so early in the season," he said.