The high-profile duo was met with a loud ovation as they walked on for Murray's first match on Centre Court since 2017. The two-time men's champion missed last year's tournament with an injury and is only playing doubles at the moment after having surgery on his hip.
"It worked out well. We've never played together, so it's always a learning curve," Williams said. "We take it very serious, so that's why we're in it."
Said Murray: "I think toward the end of the match, when you're kind of in control on the scoreboard, it's easier to sort of relax and enjoy it. Whereas the first set, we were obviously taking it seriously to win. Had a bunch of chances, didn't get them."
The partnership caused a stir at the All England Club this week after it was revealed that Britain's Clarke ditched regular doubles partner Harriet Dart via last-minute text message in order to play with the teenager.
"It was super fun to play with him," Gauff said afterward. "I hope we can play again together in the future."
Asked if he had spoken to Dart since, Clarke said: "Everything is fine. I think the media obviously did a pretty good job of making it bigger than what it was. It happens like that."
Teenager Gauff has been a sensation at the London Grand Slam. She became the youngest player in the Open era to qualify for the main draw before going on to beat five-time champion Venus Williams in the opening round.
Her run has drawn attention from outside the sports world. Gauff said Friday that she was "screaming" to receive an Instagram message from Beyonce's mother, and on Saturday she addressed being tweeted about by former first lady Michelle Obama.
"I was super-excited," Gauff said of the Obama tweet. "She's one of my role models, so it was just cool to see that she knows I exist."
ESPN's Rob Bartlett and The Associated Press contributed to this report.