The 35-year-old briefly came under pressure when Lee fought back from 8-3 to 8-5 at the mid-session interval, but breaks of 74 and 81 saw him make sure of his place in the second round.
Higgins now takes on Rory McLeod, the man accused by his first-round victim Ricky Walden of utilising “painful’’ tactics which would kill the game if every player adopted them.
The world number one and world champion from 1998, 2007 and 2009 thinks 40-year-old Englishman McLeod probably did not deserve those comments.
“He’s maybe been unfairly criticised,” Higgins said. “There was lots of tension from Rory because he knew the TV cameras were on him and he wanted to do himself justice.
“I’m expecting Rory to come out and play a lot better in his second match.’’
Earlier, Mark Selby completed a 10-1 victory over Crucible rookie Jimmy Robertson.
He faces Stephen Hendry in the second round but will not fear the seven-time champion, having beaten him at the same stage last year.
Elsewhere, Welshman Mark Williams tested the Crucible speed guns when he sprinted into a 7-1 lead against Jamie Cope in the first second-round match to get under way.
The Welshman’s potting exhibition was briefly interrupted when Cope pulled a frame back, but Williams, champion in 2000 and 2003, reeled off a further three in a row inside 32 minutes to close in on the quarter-finals.