Victoria Azarenka ended the giantkilling run of Sloane Stephens to keep the defence of her Australian Open title on track.
It was far from straightforward for the top seed, however, who wasted five match points and suffered a fitness scare before emerging a controversial 6-1 6-4 victor.
Stephens' victory over Serena Williams on Wednesday seemed to take its toll on the 19-year-old in the early stages but she grew into the contest and was starting to get on top before Azarenka limped over the line, aided by a medical time out at a vital juncture.
Azarenka dropped just three points on serve in the opening set and she clinched it with a third break drawing her opponent into the net before delivering a brilliant top-spin lob over her head for a winner.
And when she swiftly moved 2-0 ahead in the second it looked plain sailing for the top seed.
But then came the injury scare as she pulled up after chasing down a wide backhand with her left ankle the area of concern. Stephens, who profited when Williams hurt her back in their last-eight clash, sensed the door may be opening once more. She broke back and then held to get it back to 2-2.
Azarenka promptly embarked on a run of nine successive points which moved her to 4-2 only to toss her away her advantage when two double faults and a mis-timed backhand gifted Stephens a break back.
Azarenka's frustration was evident but, rather than pin her down, the inexperienced Stephens let her off the hook, playing an error-ridden game in which the world number one did little to earn her break.
Serving at 5-3, the 2012 champion wobbled horribly and saw five match points come and go as Stephens fought bravely although she was helped by Azarenka's fragile mental state.
Then came the controversy as Azarenka took a near 10-minute medical time-out for an unspecified injury seemingly unrelated to her ankle. When she returned she regained her composure and broke at the first opportunity to set up a clash with Li.