Martin Klizan edged Alexei Popyrin in the Sydney International first round, while Jordan Thompson advanced on Sunday.
Klizan was pushed by teenager Popyrin before scraping through 7-6 (7-4) 4-6 7-6 (7-5) at the ATP 250 event.
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Australian wildcard Popyrin was left to rue a slow start to the final-set tie-break, losing the first five points before being unable to recover.
In the day's only other main-draw match, another Australian wildcard, Thompson, was too good for Adrian Mannarino 6-3 6-3.