The Mexican entered the race under a cloud after his spectacular last-lap collision with Felipe Massa in Canada.
That incident - for which Perez was blamed - landed the 24-year-old a five-place grid penalty for Austria. He has also faced criticism from his fellow drivers during the past fortnight, particularly Massa, who branded him "dangerous".
But by starting on the soft tyre and running a counter-strategy, Perez was able to produce a clean race and climb from 16th on the grid to sixth at the chequered flag, finishing well ahead of team-mate Nico Hulkenberg. He also briefly led before making his pitstop.
“Today we got a very positive result for the team, especially considering where we started the afternoon," reflected Perez afterwards.
"When you start in 16th it is always going to be difficult to make up ground, but I had a very strong start and made up a good few positions. It was especially important to pass Jenson [Button] because he was on a similar strategy to mine: it was a key moment for my race.
"The only regret is that without the grid penalty I would have been further up the grid, which would have made a big difference because we had the pace to fight for a podium today.
"It's nice to be back in the points after two disappointing races: the car is improving and we are in good shape.”