Federer, the No. 2 seed, got by seventh-seeded Jo-Wilfried Tsonga 7-6 (7-4), 4-6, 7-6 (7-4), 3-6, 6-3 well after Murray had dispatched unseeded Jeremy Chardy 6-4, 6-1, 6-2.
Tsonga had more breaks than Federer (5-4) and that allowed him to take the second and fourth sets. Federer, however, still won nearly 70 percent of the points on serve overall. He lost just five points serving in the fifth set and used a quick fourth-game break for the advantage in the fifth set.
Tsonga fought off four match points before holding serve in the eighth game but Federer fired a forehand winner to get to a fifth match point and put Tsonga away with an overhead.
Federer's win puts him into the semifinals for the 10th consecutive year at Melbourne. He won the tournament in 2004, '06, '07 and '10. He lost in the semis the last two years.
Murray gained his eighth semifinal berth in the last 11 Grand Slam events. He has appeared in the last four Australian Open semis, losing title matches in 2010 -- to Federer -- and 2011 and the semifinal in 2012.
He had 32 winners against 20 unforced errors in beating Chardy. He did drop serve twice but piled up eight breaks, winning 53 percent of the points off Chardy's serve.
Murray owns a 10-9 lifetime advantage in matches against Federer. Last year, Federer took finals from Murray at Dubai and Wimbledon while Murray beat Federer in the gold medal match at the Olympics.