The Thai siblings who entered the maindraw as lucky-losers were in charge in the opening set before their opponents managed a crucial break in each of the last two sets.
Meanwhile. Juan Martin del Potro admitted he felt "alive again" after the injury-plagued former US Open champion sent Swiss fourth seed Stan Wawrinka crashing out of a wet and wild Wimbledon on Friday.
On a day when rain caused a 10th delay of the week, forcing organisers to consider playing on the middle Sunday for the first time since 2004, the giant Del Potro shone beneath the Centre Court roof.
Playing in his first Grand Slam tournament since the 2014 Australian Open, his 3-6, 6-3, 7-6 (7/2), 6-3 second round victory over Wawrinka brought back memories of his stunning 2009 US Open win before a series of wrist injuries pushed him to the brink of retirement.
The world number 165 from Argentina, who was a semi-finalist in 2013 in what was his last appearance at Wimbledon, next faces French 32nd seed Lucas Pouille.
"It feels amazing, it's a great sensation," said the 27-year-old who has undergone three wrist surgeries in the last two years.
"I enjoyed the crowd. It's an incredible feeling, that's why my hands are still shaking.
"I feel alive again. After sitting at home for two years, this feels like a second or third career," added the former world number four.
Wawrinka, a quarter-finalist in 2014 and 2015, fired 47 winners past Del Potro but was undone by 48 unforced errors.
"We are happy that he's back. He's a great guy off the court. He's amazing player on the court. He's big champion," said Wawrinka.
On the women’s side, defending champion Serena Williams said she was ready to kick up a racquet at Wimbledon after smashing one up on court.
The world number one, who is fighting for a seventh Wimbledon singles title, said she was angry and ready for any challenge after narrowly surviving a major scare against US compatriot Christina McHale on Friday.
Williams was so incensed with her own performance that she violently smashed her racquet repeatedly into the Centre Court turf.
But she was able to dig deep and make it through to the third round, where she will face Germany's Annika Beck.
"I've struggled and fought on every surface and I've come out on top," the 34-year-old said.
"Every match I do plan on getting better. I hope to play more matches to get better. I'm ready for any challenge.
"I'm amazing when it comes to tight matches and getting through it, just really fighting till the end. I don't give up," she said after coming from behind to beat world number 65 McHale, 6-7 (7/9), 6-2, 6-4.
"I was definitely in warrior mode. I was out there playing for my life at that point, trying to play to stay in the tournament," said Williams, who is trying to win a Open Era record-equalling 22nd Grand Slam title.
"I've been through a lot in my career, on the court and off the court. I've been in every position you can be in. So I know mentally I'm, hands down, one of the toughest players out here. It's very difficult to break me down mentally."
- Racquet abuse -
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After losing the first set tie-break, Williams was given a warning after smashing her racquet into the ground five times after sitting down, before letting go -- the racquet flying into the stomach of a television cameraman.
"I was just really, really, really angry. I had a lot of chances," said Williams.
"I was a little disappointed in myself at that point. It's definitely a fine.
"I've cracked a number of racquets throughout my career. I've gotten fined a number of times for cracking racquets. In fact, I look at it like I didn't crack one at the French Open or Rome, so I was doing really good.
"I don't want to go too long without cracking a racquet. I'm on track. I try to crack a certain amount a year. I'm a little behind this year, so it was good."
Her sister, five-time Wimbledon champion Venus Williams, reached the last 16 on Friday, seeing off Russian teenager Daria Kasatkina 7-5, 4-6, 10-8 in a tie featuring a rain stoppage when she held match point.
The eighth seed, 36, was 7-6, 40-30 up on Kasatkina's serve in the final set on Court One when the tie was halted by the second rain delay of the day.
The two sisters could only meet in the Wimbledon final due to being in separate halves of the draw.
"I'm just glad I don't have to play her in the fourth round, as I do at every Grand Slam," Serena said.
"That's the only thing I'm just happy about. Obviously I'm happy she's won. But I'm just happy I don't have to play her.
"I approach it now as any other match. But in the beginning, obviously I wasn't able to approach it like that.
"Now it's different. It's like, Okay, she's probably my toughest opponent, hands down, that I've ever played. It's never exciting to go against her."