Brown, a German-Jamaican with dreadlocks reaching down to his waist, is one of tennis’ born entertainers and the unorthodox nature of his game can cause problems for the best.
He famously beat Rafael Nadal at the same stage of Wimbledon two years ago, while Murray’s defeat to Brown’s serve-volleying compatriot Mischa Zverev at the Australian Open in January would have given him encouragement.
But Centre Court is Murray’s stage and the world number one did not allow himself to be bullied.
Tennis players love rhythm and Brown provides none, mixing 128mph second serves - his fastest serve was a second serve - with languid volleys and drop shots before throwing in a thumping backhand or two.
But Murray has some of the best hands in the game and was rarely outmanoeuvred.
The victory maintains the 30-year-old’s record of never having lost before the third round of Wimbledon, and he moves through to a meeting with flashy Italian Fabio Fognini on Friday.
Murray said: “I felt the momentum was with me, I was starting to see the shots he was going to play a little bit quicker and that allowed me to get to some of the drop volleys and also to come up with some good passing shots.
“I played well. The last three games I didn’t serve particularly well, but the rest of the match I served well, I was getting a lot of free points there, serving a lot bigger than I was in the first round which is good.”
Asked about his hip, Murray told the BBC: “It’s okay. I’ve moved well the first couple of matches. It hasn’t affected me. I’ve been getting good practices in and I feel good. Hopefully it stays that way.
“So far I’ve been very happy with how I’ve been feeling on the court. It’s been a good start and hopefully I can keep it going.”
Stan Wawrinka’s conqueror Daniil Medvedev has apologised for throwing money at an umpire’s chair at the end of his second-round defeat to Ruben Bemelmans.
The Russian created one of the stories of the opening day of Wimbledon when he slayed three-time grand slam champion Wawrinka on Centre Court but courted controversy in the second round after losing in five sets to Belgium’s Bemelmans on Court 16.
Medvedev ended the match in disgrace as, after taking exception to some of the decisions by umpire Mariana Alves, he took coins out of his wallet and threw them at the foot of the umpire’s chair.
The 21-year-old insisted he was not insinuating Alves had been bribed and accepts his actions were wrong.
“I was disappointed with the result of the match,” he said. “It was frustrating after a big win I had. All the match was not going well for me, so I was just very disappointed.
“In the heat of the moment, I did a bad thing. I apologise for this.”
Meanwhile in the women’s tournament Petra Kvitova could not live up to her billing as one of the Wimbledon favourites as she crashed out in the second round to Madison Brengle. The Czech, who ended the match in distress having had her blood pressure taken, had poured scorn on suggestions she could win Wimbledon just six weeks after returning to action following a knife attack.