Baker had never previously qualified for a Grand Slam event

The British number three kept cool despite some gamesmanship from the Austrian to book his Melbourne berth.

"I'm delighted - it is a huge step in my career to do that as I have beaten three really good players to qualify," said the 21-year-old Scot.

Baker faces big-serving Croatian 20th seed Ivo Karlovic in the first round.

He showed his maturity as Koellerer tried to put him off his stride in their match.

Koellerer hit an under-arm serve in the fifth game of the first set, and took an injury time-out when Baker was one point away from a crucial break in the second.

But Baker knew what to expect having spoken to several players in the locker room about the Austrian's tactics.

"It was difficult, but I was expecting it as the players told me in the locker room how he tries to bend the rules," he said.

"The best way for me to go about it was not to give him any energy and focus on my game."

Baker, who will be part of Great Britain's Davis Cup team in Argentina next month, felt his attempts to qualify for the Heineken Open in New Zealand last week had helped him to progress in Melbourne.

"I had the three matches in Auckland and I felt I learned a lot from them," he said.

"I managed to switch on immediately and kept going. I served well today and that made a big difference for me."