After seeing their compatriot brushed aside in the opening set, few in the crowd could have predicted what would transpire over the next couple of hours, Paszek coming within a whisker of victory only to be denied in the tensest of finishes.
Paszek had her chances, holding a match point in the decider, but Knapp showed admirable resolve herself to dig in and prevail, 6-0, 6-7(5), 7-6(6).
"It was a big fight and in the end I finished the match a little bit better," Knapp said. "At the beginning it was not really a fight, I was serving well and there were not a lot of rallies, but Tamira found a way back into the match.
"If you win matches like this, fighting and saving match points, it's good, but let's hope I don't have to do it again!"
Former World No.26 Paszek has struggled for fitness and form in recent years and was disappointed yet philosophical following her near miss.
"A victory in a match like this would have been one of the most emotional moments in my whole career - especially in front of my home audience," Paszek, whose last WTA main draw win came 14 months ago, said. "The support of the people gave me chills at times.
"It hurts when you see that you're so close to beating a Top 50 player and you still lose."
After the rain 24 hours earlier, the tournament organizers were forced to play catch-up on Tuesday, somehow squeezing in 10 more opening round clashes. Among those progressing were Samantha Stosur and Julia Goerges, who won in contrasting fashion.