Erakovic was good against Radwanska, hitting 35 winners and only 15 unforced errors, but still had to come from a break down in each set to win.
She trailed 4-2 in the first set before rattling off four-straight games and was also a break down in the second before breaking Radwanska twice to take the match. She had 11 break point opportunities in the match and converted four.
The match started in hot, dry conditions but rain soon threatened, which made the court heavier and meant Erakovic's serve didn't hold as much venom as it might normally have. She had to rely on her forehand and also tried to get to the net as often as possible.
"I felt from the first game or first few games that it was really close tennis," Erakovic said. "She was playing well and I felt our level of tennis was very high and it was very tough and I'm pleased that I got through today."
Erakovic has never played Vinci in singles and the Italian proved she is in good form with a comfortable 6-2 6-4 victory over Australian Ashleigh Barty in her first-round encounter.
Erakovic's win saw her pocket $46,000 and take her year's earnings beyond US$230,000. She has had a good year, rising to a career-high 39 in May after making the final in Memphis and semifinal in Budapest, but she had lost in the first round in four of her previous six tournaments.
A good performance at Wimbledon will also put her in a good space ahead of next month's London Olympics, which are also being played on Wimbledon.
"There's always good memories for me here at Wimbledon," she said on the eve of the tournament. "I really appreciate the history. I have always liked grass and the history here. My first coach [Chris Lewis] made the final here ... It's a special place. It's going to be interesting to have the Olympics here and everyone wearing coloured clothes, too."