The Belgian, a three-times grand slam champion and Melbourne runner-up in 2004, sealed a tough victory a little after midnight local time with a drilled backhand crosscourt.
"She was unpredictable," Clijsters told reporters. "I had to get a feel for it.
"In the second set I started being a bit more aggressive. I had to really step it up and finish it off," added the tournament favorite.
Clijsters squandered an early break gifted to her by a nervous Makarova and was forced to a first set tiebreak, which she took 7-3.
Normal service resumed in the second set, although Clijsters needed to take anti-inflammatory pills for a tight hamstring in a minor scare.
However, she had already found the range with her heavier groundstrokes and broke the Russian twice to set up a clash with Polish 12th seed Agnieszka Radwanska.
"At important moments, like in the tiebreak, she played unbelievable -- fighting for every point," said the 49th-ranked Makarova after her best grand slam run to date.
"I just have to go for every ball because if I wait for a mistake from her, I have no chance to win. She was better on the big points."