In four of the best points seen at Wimbledon so far, Brown responded with a half-volley victor off his toes and a fine angled volley.
A smiling Brown shrugged at that rapid-fire entertaining exchange that gave the top seed another break and 5-2 second-set lead.
The pair have never met on grass, though, and Murray showed fine form against Brown, while he will also have plenty of home support.
How did he reach the third round? Fognini has had back-to-back effortless six sets, as he's coming off a match that took less than two hours and he hit 60 winners. On Wednesday he was far too inconsistent and even with his suspect hip, Murray ran down most of his drop shots. She played really well last week in Eastbourne. Once he gets ahead he's not an easy guy to break.
Five-time champion Williams is trying to concentrate on tennis against the backdrop of the impending legal action she faces back home in the United States over a fatal auto crash.
Kvitova, playing in her second Grand Slam since recovering from a terrifying knife attack in her home, needed medical assistance during the third set.
Brown, who beat Rafa Nadal here in 2015, had said before the match that he was confident of winning Centre Court's support, even ahead of one of Wimbledon's favourite sons, and the great entertainer was soon pointing to the crowd and milking the applause after leaving Murray stranded at the net with a ideal lob.
The Championships may pride themselves on history and consistency - from the draconian all-white dress code to the strict rules on advertising around the grounds - but serve-and-volley is one tradition that looks unlikely of returning anytime soon. "Like before the French Open, when I'm in a "terrible" place in terms of my game and I'm not playing well, having that little bit of extra motivation can help".
Murray said: "I think he's always unsafe. I don't have much to lose", Vekic said.
"I had a great day yesterday and obviously a worse day today and tomorrow's another day". It's going to be very hard.
He next faces Spanish 18th seed Roberto Bautista Agut who ousted German qualifier Peter Gojowczyk.
Former French Open champion Francesca Schiavone bid farewell to the All England Club after she was beaten in straight sets by fourth seed Elina Svitolina, while recent titlist Jelena Ostapenko came from a set down to defeat qualifier Francoise Abanda and reach the third round.
"It's a good thing when there are more Brits around", Murray said. But, yeah, I mean, he certainly can play well.
"Fognini is an incredible shot maker, but he's a slightly different sort of player to Dustin and Bublik". He said: "Everybody has got to focus on themselves but I feel part of something bigger".
"I think he's always risky", said Murray, who faces Fognini on Friday on Centre Court. 'In Rome I play at home, so I play a really good match.
Gilles Muller outlasted Lukas Rosol 7-5, 6-7 (7-9), 4-6, 6-3, 9-7 over nearly 3¾ hours, while American Sam Querrey stopped Georgian Nikoloz Basilashvili 6-4, 4-6, 6-3, 6-3. "But here, it's completely different". Of course, it's Wimbledon. It's best-of-five. He's the defending champion.
More succinctly, Brown concluded in an echo of a familiar football chant: "That's why he's champion". So it's going to be really tough, for sure. "He's the favorite. Nothing to say". Sometimes he hits two first serves, goes for a huge second serve. "He's the favourite, but I think I have the game to play against him, hopefully to play my best tennis another time, try to complicate his life on court".