"When I was down I was just thinking 'dig in' and it's amazing what you can do when you just keep believing and keep battling away.
"I was very calm at that point and I executed really well on those points. Once I'd saved them and broken back it was a massive turning point."
She added: "I started the match badly because I wasn't feeling great early on, but I knew I would rally a bit as the match went on and I started to feel better. She is very, very tough so it's a great win.
"This is always a special tournament for me and it's going to be even more special after this."
Baltacha will again be the underdog in round two when she faces world number 15, Pennetta, who won their only previous encounter at Wimbledon back in 2000.
"I'm looking forward to playing Pennetta," said the Scot. "On paper she beats me every time but she hasn't played a match yet and I'm going to go out there with lots of confidence and nothing to lose.
"It should be a good match."
Baltacha's victory keeps British interest alive in the women's singles after Anne Keothavong and Heather Watson both lost in the qualifying tournament on Monday.
Andy Murray is seeded fifth in the men's event and plays later this week.
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