Fresh from suffering a 6-0 defeat to world champion O'Sullivan in only 68 minutes at last month's UK Championship, Milkins looked destined to suffer another whitewash, but somehow managed to snatch the sixth frame with a highest break of 47 after O'Sullivan had broken down on 53 when seemingly poised for victory.
Supported by an animated, boisterous sell-out crowd of 1500 that included friends Wood, the artist Damien Hirst and six-times World Championship finalist Jimmy White, O'Sullivan never needed to be at his best as runs of 48, 40, 84, 42, 42, 91, 62 and 59 carried him into a 5-0 lead that quickly turned into a 6-1 drubbing in his first match at the invitational event in two years.
O'Sullivan will face Barry Hawkins or Ricky Walden in Friday's quarter-finals.
"It is not every tournament you play in London," said O'Sullivan. "You just have to get your head around it. I didn't want to let people down.
"Ronnie (Wood) enjoys it wherever he goes. He is just high on life that guy.
"It is good that Ronnie came. I haven't seen him for a while.
"He is in great form, and loves his snooker. There have been plenty of times he has got his white gloves out to referee for me and Jimmy (White).
"He was having a go tonight when Damien was getting the balls out for me during practice. He was saying: 'Where are your white gloves?'
"He's always got the white gloves out when he is doing his referee bit.
"He is just a just a huge snooker fan. It is nice. Jimmy (White) is my hero and father figure, and it was fantastic to see him here tonight.
"He's been there for me more than any other snooker player. It has been a good night. It was like a good night out at the pictures for my girlfriend, friends and family."
O'Sullivan skipped the Masters during his year-long sabbatical from the game last season, but admitted his attendance at the semi-final between Mark Selby and Graeme Dott had convinced him to return a year ago.
"In the end, I didn't really watch any snooker last season, but this is the tournament I came to pick my mate up at," said O'Sullivan.
"It made me think that I was missing a lot of the guys at the tournaments so this was one of the catalysts that made me think about coming back.
"And also the school fees..two reasons there."
O'Sullivan did sympathise with Masters debutant Milkins as he struggled to cope with the nature of the crowd.
"It was a tough match for Robert to get into, and I know how he felt with the crowd." commented O'Sullivan. "I'm just pleased to get the win.
"If you give any of the players a lead in this tournament, they are top players. They are all top players for a reason. "