This is familiar territory for Konta and Evans but very much new ground for 22-year-old Dart, who followed up her first Wimbledon singles victory on Tuesday by beating Beatriz Haddad Maia 7-6 (4) 3-6 6-1.
Having served for the first set and then come through in a tie-break, Dart was pushed to a deciding set but swept through it to set up a third-round clash with top seed Ashleigh Barty.
Dart said: "I think I'm just learning from all these experiences that I'm having this year. Everything is still pretty new for me.
"This is my second Wimbledon. I'm still finding my feet. I'm definitely proving that my tennis is right up there with the level. I'm just doing the best that I can. I'm just really excited to play my next match."
Konta has loftier ambitions than the third round but she has done her job very professionally so far and barely put a foot wrong in a 6-3 6-4 victory over Czech Katerina Siniakova.
Next for the British number one comes what will be a third clash in two months with ninth seed Sloane Stephens.
Konta came out on top at the Italian Open and the French Open on clay and will now try to complete the hat-trick on grass, which should favour the British player.
"I think records don't necessarily mean a lot when you step out onto the court," said Konta. "I think Sloane is one of the best players in the world. She's a grand slam champion.
"Every time we step out onto the court, it's 50/50. It is a nice change playing her on the grass this time. We're kind of going through all the surfaces, which is fine."
Evans was overcome with emotion after beating 18th seed Nikoloz
Basilashvili in the best moment of his comeback so far.
The British number three has matched his most successful run at Wimbledon and is closing in on a return to the top 50 just over 12 months after returning to the sport without a ranking following his year-long cocaine ban.
After sealing a 6-3 6-2 7-6 (2) victory on Court Two, Evans thrust his hands to the sky with tears in his eyes.
"I just want to do well at this tournament," he said later.
"It was a goal to be in the main draw here. I did that. Obviously I missed out the last few years. To be into the third round is great for me.
"A lot of my friends were here, people who have helped me so much. It just got the better of me today. There's plenty more tennis to be played in this tournament, so I won't be resting on that win."
Clarke acquitted himself well, pushing the eight-time champion to a tie-break in the second set before falling to a 6-1 7-6 (3) 6-2 defeat on Court One.
The 20-year-old, who won his first match at Wimbledon on Tuesday, is coached by his brother and sister, who were both watching along with other members of his family.
He said: "I think it probably means more to them at the minute than it does to me. I'm the youngest in my family, so for them to see the baby playing Federer on Court One, it's a big thing."
British number two Norrie made his Centre Court debut and led 4-2 in the opening set against eighth seed Nishikori before losing 6-4 6-4 6-0.
"I don't think I was really too fazed by the occasion, but a phenomenal
experience today," said the 23-year-old. "I was just really happy with the way I handled myself."