Kerber looked in danger of getting beaten in the final set. However, the German responded to the crisis magnificently, taking the final five games to close out a 6-2, 5-7, 6-2 victory.
In the second round, she will face compatriot Carina Witthoeft.
"I have to say I'm really happy to be back here. Everything started here for me when I won my first Grand Slam here," Kerber said after her match as quoted by Women's Tennis Association (WTA). "The first round is always tough, but I just tried to enjoy it as much as I could. I'm so, so happy to be in the second round."
It has been a tumultuous start to the year for the No.1, who arrived in Melbourne short of match practice following early defeats at both Brisbane and Sydney tournaments.
This did not appear to be an issue early on as she sauntered into a commanding lead in front of an appreciative Rod Laver crowd.
Yet from 5-3 ahead in the second set, the wheels began to come off. The following game, Tsurenko saved a match point and then drew level when an increasingly rattled Kerber slapped a forehand into the net. Soon they were heading into an improbable third set and the Ukrainian began to sense an upset.
But Kerber rallied to avoid a big upset.