MELBOURNE, Australia — Serena Williams took a big step toward winning a record-tying 24th Grand Slam singles title Monday, defeating the top-seeded Simona Halep, 6-1, 4-6, 6-4, in a round of 16 slugfest.

“It was really an intense match, some incredible points,” Williams said in an on-court television interview afterward. “I really needed to elevate my game. She is the No. 1 player in the world and there’s a reason.”

Williams, 37, looked a step slow at the start of the match, losing the opening game with uncharacteristically poor shotmaking and errors. But then she turned on the jets, playing with power and precision, and not allowing her Romanian opponent to find her usual rhythm.

Halep, 27, fought back gamely, coming back from an early break of serve to take the second set.

By the third set, the points began to be played with longer rallies. Williams broke serve midway through that last stanza. She closed out the match on serve, with little resistance from Halep.

The match, played before a packed crowd of 15,000 at Rod Laver Arena, was a rare instance in which a top-ranked player was seen as the underdog. Williams had dominated their career head-to-head record, winning eight times and losing once.

If Williams wins the Australian Open this year it will be her 24th Grand Slam title, tying the record by Australian Margaret Court. Court won her titles in both the amateur and professional era, which began in 1968.