Britain's Andy Murray won his first Grand Slam match since becoming world number one but was given a stern test by world number 95 Illya Marchenko.
A clearly frustrated Murray was far from his best but reached the second round of the Australian Open with a 7-5 7-6 (7-5) 6-2 win over the Ukrainian.
The Scot, attempting to win his first Australian Open title after five final defeats, won in two hours 48 minutes.
The 29-year-old Wimbledon champion faces Russia's Andrey Rublev next.
First-round exit for Bedene
British number four Aljaz Bedene lost 7-6 (9-7) 7-5 0-6 6-3 to 36-year-old Dominican Victor Estrella Burgos.