Britain's Heather Watson beat Jamie Lee Hampton of the United States 6-1 6-4 to become the first British woman to reach the Wimbledon third round since 2002.
Watson, who had never progressed further than the second round at a Grand Slam, won the first five games to take control of the match on Court Two.
The 20-year-old from Guernsey will play Polish third seed Agnieszka Radwanska next.
The last British woman to reach the third round was Elena Baltacha in 2002.
On day one, Watson, ranked 103 in the world, beat experienced Czech Iveta Benesova to become the first British woman since Jo Durie in 1985 to win a match on Centre Court.
"People might say on paper it was a good draw, but she made it hard for me and wasn't giving me anything," the British number four told BBC Sport.
"I don't think Jamie was at her best at the beginning and I tried to take advantage of that.
"All I was saying to myself [on match-point] was 'don't double-fault', but I stayed calm and stayed focused and knew I had to go for it."
Watson insisted she would not be worried by the prospect of taking on Radwanska, who has twice made it into the last eight at the All England Club.
"It's definitely not terrifying. It's exciting. I'm looking forward to it and I'm relaxed about it as well," she added.
Watson went into the match ranked three places lower than her opponent but looked a class above in the first set.
Hampton, perhaps overwhelmed by the extra attention on Court Two, was broken in her first service game and lost the first set in only 28 minutes.
The American gave a better account of herself in the second set but Watson converted her second match-point to advance.
Watson, who will now seek to become the first British woman to reach the last 16 since Sam Smith in 1998, believes she is playing well.
"I always knew I could play this well, I could get far in these tournaments, but it's different playing like that in practice than bringing it onto the match court at big occasions with pressure," she said.
"So I'm just pleased that it's finally clicking for me."
In the men's draw, Jamie Baker lost 7-6 (7-1) 6-4 7-5 to three-time finalist Andy Roddick on Court One.
Play resumed on Wednesday with Baker trailing 4-2 in the second set and the American had too much experience for the British number three.
"At the moment it stings because I lost even though it was quite evenly matched," said Baker, who has jumped from 478th to a career-high ranking of 186th in the last 12 months.
"The biggest thing I will take out of this is that I didn't feel like I was invading someone else's territory. I am now playing tennis of a level that is well inside the top 100 now.
"How many times has Andy Roddick played on that court? His record in Slams is immense. I am looking forward to watching the tape of it because I'd say it looked quite even throughout."
It was a mixed day for Great Britain in the doubles competition.
Jamie Delgado and Ken Skupski overcame Matthias Bachinger and Tobias Kamke 6-3 5-7 6-3 6-4, but 13th seeds Colin Fleming and Ross Hutchins went down 3-6 4-6 6-2 7-6 (7-5) 6-3 to Mikhail Kukushkin and Lukas Rosol.
Josh Goodall and James Ward were beaten in straight sets by eighth seeds Aisam ul-Haq Qureshi and Jean-Julien Rojer, and Londoner Dominic Inglot and his partner Treat Conrad Huey also departed in the first round.
In the women's doubles, Anne Keothavong and Elena Baltacha, both through to the second round of the singles competition, were soundly beaten 6-3 6-2 by the 15th seeds Irina-Camelia Begu and Monica Niculescu.
Baltacha and Keothavong, along with Andy Murray and James Ward, are in singles action on Thursday.