Perez missed the Thursday media day to rest after falling sick on Wednesday night.
He then underperformed during the Friday qualifying session for the full grand prix by exceeding track limits through the final two corners to have three lap times deleted for a Q2 exit.
But after finishing second in the sprint race, Perez then climbed from 15th to complete the Red Bull Ring podium on Sunday behind team-mate Max Verstappen and Charles Leclerc.
The Mexican was aided by drivers ahead being hit with five-second track limits penalties that were served during their pitstops, but he notably battled past McLaren driver Lando Norris and Ferrari rival Carlos Sainz during the final stint to secure third place.
Perez reckoned his comeback was particularly satisfying given his illness, the effects of which included a lack of strength, sleep and "high fevers".
He said: "I'm really happy. It's been a very difficult weekend for me personally, physically.
"I have been really, really weak. I was sick on Thursday. So, it hasn't been an easy weekend.
"High fevers, no sleep, during the weekend. So, a great recovery from the team, fantastic strategy and we had great pace."
Perez said of the result that ends a run of three GPs without a podium: "It's been a bit of a rough patch for me. So, now, hopefully we are back and we can keep those positions here now."
Verstappen, who claimed the sprint race and GP poles, both wins plus gained a bonus point for setting the fastest lap over the line, reckoned his team had delivered "perfect stints".
This execution, he reckoned, left him confident that he could repass both Ferraris to secure his 42nd win after Leclerc used a virtual safety car to pit early and his superior race pace enabled him to take the lead once Verstappen finally made his first stop.
But once Verstappen switched to hard tyres, he required only 10 laps to close a six-second gap to Leclerc and pass for the eventual victory.
Explaining the strategy, Verstappen said: "We opted not to box during the virtual safety car, and just follow our normal strategy.
"I think that worked out really well, because the tyre life was not that high around here. I think our stints were perfect."
He added: "I could see already the few laps before the virtual safety car came out. We were pulling out quite a gap.
"So, I knew that I would get them back eventually. I think just following our own plan at the time was the best way forward."
