The Rocket picked up where he left off after leading 10-6 overnight, securing the win by taking three out of the first four frames on Monday afternoon, leaving no room for a comeback before the planned break.
The victory keeps O'Sullivan on track for a history-making eighth World Championship title – a record in the modern era.
In 2022, he tied the legendary Stephen Hendry's record of seven championship wins.
It also keeps the world number one in the hunt for a historic Triple Crown sweep – winning all three of snooker's most prestigious events (World Championship, UK Championship, The Masters) in a single season for the first time.
"If I'd not been as tight or as clinical in some situations, he would probably have got on more of a roll at times," O'Sullivan told BBC Sport.
"I was pleased to be able to stem that at points and try to have an impact when I got a chance.
"Early days for me, trying this new way of playing, different style of cueing, just to get away from the 'yips' as I call it, the easiest way of explaining it.
"It's been hard work for two years and I decided I couldn't continue playing like that, so I had to make some changes, so it's the body and mind trying to catch up with each other.
"I've got some of it right, it's just the other pieces need to fall in - I'm trying to work out the puzzle."
O'Sullivan's next opponent will be either Jack Lisowski or 2015 champion Stuart Bingham.
Meanwhile, Kyren Wilson also secured his place in the quarter-finals with a commanding 13-6 win over debutant Joe O'Connor, setting him up for a clash with either Mark Allen or John Higgins.
O'Sullivan's comfortable progress through the tournament continued after his first-round 10-1 demolition of Jackson Page.
Against Day, an opponent with a 13-year losing streak to O'Sullivan, the fan-favourite rarely looked to be in any trouble.
His relaxed demeanour was even captured when he shared a laugh with a passionate fan during a shot in frame 17.
