The two players were locked at a set apiece and 1-all in that decider when Pereira took it to a whole new level, reeling off five games in a row to win after two hours and 36 minutes, 6-4, 4-6, 6-1.
Earlier this year, by winning the Claro Open Colsanitas in Bogotá, Pereira became the third Brazilian in the Open Era to win a WTA title, after Maria Bueno (who won three) and Neige Dias (who won two).
A Brazilian winning in Brazil is even rarer, though. Pereira is just the second Brazilian in the Open Era to win a WTA title in Brazil - Dias achieved the feat once, doing it over in Guaruja in 1987.
"I have no words to describe what I'm feeling right now," Pereira beamed. "When I came here I didn't know if I would be able to play - my knee wasn't so well - so I can't believe I managed this victory.
"It's the best day of my life. I'm living a dream right now."
There was an even deeper happiness to the victory.
"My family has a very beautiful history, from where we came from and everything we've managed to achieve, everything we've battled for. I've passed some very difficult moments in my life, injuries and everything else, so to come back has been difficult but I'm very happy I've been able to do that.
"Something that inspires me is when people call me a warrior. It describes me perfectly. I know I don't have the best forehand, or the best backhand, but I feel privileged to have this characteristic.
"I fight until the end. I never quit."
Beck won't leave Florianopolis empty-handed, though - on Friday she won the doubles title. Seeded No.4 alongside fellow German Laura Siegemund, she rallied from 3-1 down in the second set - and saved set point in that second set - to edge No.2 seeds María Irigoyen and Paula Kania, 6-3, 7-6(1).
It was Beck's first WTA doubles title, while Siegemund won her second WTA doubles title.
"I had a really good week. I won my first doubles title and the singles final means a lot to me," Beck said. "Teliana started to play much better in the third set than in the second set, and I really want to congratulate her for the victory. She played great tennis all week and really deserves the title.
"It was a great final at a great level, and I'm really happy with my whole tournament."
Obrigada mãe. Conseguimos!! Te amo demais!! pic.twitter.com/5KFzKqNSo4