A strategy blunder in the wet-to-dry Q1 qualifying session at Portimao last weekend left Rins at the back of the grid in 23rd, but a stunning start in Sunday's race led to him jumping up to 11th on the opening lap.
Rins' march continued in emphatic fashion as he carved through to fourth by the chequered flag, missing the podium by just 3.5 seconds as his front tyre cried enough in the latter stages.
The three-time race winner now sits second in the standings equal on points with new leader Fabio Quartararo following his Portugal win.
"Yes, sincerely it was a good race. We finished quite in the front, we took a lot of important points," Rins said.
"But for me it was a good race. I was believing [I could fight back] - not many people were believing in me that I could do a good race.
"But anyway, I tried till the end. When I tried to overtake Aleix [Espargaro] my front tyre was a little bit destroyed and I started to feel a big drop.
"So, I preferred to remain [behind], to stay fourth. Good points for the championship."
This result continues a strong start to the season for Rins and comes off the back of a similarly strong charge from seventh to second in Austin.
Asked what the most important thing was from his Portugal race, Rins replied: "What is good is the final position and my faith, my strength to be there.
"As I said before, not many people around me were believing, were pushing me.
"For sure, today I saw more guys here [congratulating me] doing the interviews, my WhatsApp is on fire.
"Yesterday nobody was saying congratulations. So, I'm happy to have people around me. So, we need to understand why on Friday the feeling was so bad."
Rins says he was able to gain so many places at the start due to his "risky" decision to go around the outside of the field at the first three corners.
His start to 2022 is in stark contrast to 2021, in which he crashed numerous times – including out of the victory battle in Portugal – while in strong positions and only managed one podium across the whole campaign.
He explains that he now has "more control of myself and my riding style", adding: "I can feel the tyres more.
"There were a couple of corners, like for example corner three and corner eight, where I was going to the limit and I was feeling how the front was closing.
"I was feeling where the limit was. Last year, to find this was more difficult."
