She dominated the second set despite the injury, allowing the Romanian player to win just six points.
Murray beat Haase 6-3, 6-1, 6-3 in the opening round and was asked what it felt like to play after his triumph at the U.S. Open, where he became the first British man since 1936 to win a major title.
"I can try and focus on the second part of my career now," he said.
The 25-year-old Murray seemed more at ease and relaxed than he had been in previous trips to the season's first major.
"It was a good start, nice to win in straight sets," he said. "It was the hottest day we've had for a while so the court was playing much quicker."
It's been 12 months since Murray started working with eight-time major winner Ivan Lendl, and he attributes much of the success in his breakthrough 2012 to his partnership with his new coach.
It's relaxed "in front of the cameras, yeah," Murray joked. "Behind closed doors he works me very hard.
"We've had a very good relationship so far. He's very honest, very open. He doesn't lie to you, he tells you exactly how it is and that's exactly what I needed."
Also advancing were No. 13 Milos Raonic of Canada, who beat Jan Hajek 3-6, 6-1, 6-2, 7-6 (0), No. 17 Philipp Kohlschreiber, No. 21 Andreas Seppi and No. 25 Florian Mayer.
In a record for the Australian Open, 42-year-old Kimiko Date-Krumm upset No. 12-seeded Nadia Petrova of Russia 6-2, 6-0 to become the oldest woman to win a singles match at the tournament.
In other women's matches, former No. 1-ranked Caroline Wozniacki won the last six games to beat Sabine Lisicki of Germany 2-6, 6-3, 6-3, and No. 16 Roberta Vinci and No. 17 Lucie Safarova also moved on. American teenager Sloane Stephens beat Simona Halep of Romania 6-1, 6-1.
Former U.S. Open and French Open champion Svetlana Kuznetsova continued her comeback from a knee injury that kept her out of the U.S. Open, ending her run of 40 consecutive majors. Also, No. 14 Maria Kirilenko had a 6-4, 6-2 win over American Vania King, and China's Peng Shuai beat Canada's Rebecca Marino 6-3, 6-0.