The top seed Andy Murray battled back from the brink for the second night in a row as he beat Luxembourg's Gilles Muller in the second round of the Brisbane International on Wednesday. Murray lost the first set against Muller and was facing two break points to go 5-3 down in the second before clawing his way back to win 4-6, 7-6 (7/4), 6-0 in two hours exactly. The 24-year-old Scotsman was in similar trouble against Mikhail Kukushkin in the first round before recovering and will be desperate to avoid another slow start against Cypriot Marcos Baghdatis in the quarter-finals. "I felt I moved better in the second and third sets and that's such a big part of my game," a relieved Murray said. "I was happy to get the win -- the more matches I can get this week, the better. "I thought once I got into the baseline rallies I felt good but he served very well, especially for the first couple of sets and I just managed to hang in." The world number four Murray, who is eyeing his first Grand Slam at the Australian Open in less than two weeks, started well and looked in complete control throughout much of the first set. But serving at 4-5 he played four poor points in a row to hand Muller the first set and the early advantage. Muller played a superb second set and used his left-handed serve with devastating effect, but Murray just managed to hold on and force a tiebreak. By that stage the Scotsman was starting to gain the ascendancy as he began to move better and serve with more purpose. Once he claimed the tiebreak Muller's challenge was as good as over. His next opponent Baghdatis earlier upset fifth-seeded Japanese Kei Nishikori 6-3, 6-4 to continue his love affair with Australia, where he won the Sydney International two years ago and reached the Australian Open final in 2006. Frenchman Gilles Simon became the first man through to the quarter-finals when he downed Australian wildcard James Duckworth 6-3, 7-5. Simon said the first tournament of the year was always one of the toughest. "I feel like it's going to be hard to beat all the players here," he said. "There are no injuries, no players are tired, everybody's playing good tennis so every match will be hard." Simon next takes on Colombia's Santiago Giraldo, a 6-4, 6-4 winner over German Philipp Petzschner. Australia's Bernard Tomic ensured a bad day for the Japanese by demolishing qualifier Tatsumo Ito 6-1, 6-2, while third seed Alexandr Dolgopolov beat Igor Andreev 6-7 (3/7), 7-6 (11/9), 6-2. Dolgopolov will take on former champion Radek Stepanek after the sixth-seeded Czech downed Finland's Jarkko Nieminen 7-6 (7/3), 6-2.