Four-time runner-up Murray finished the stronger, beating the eighth-seed 6-3, 6-7 (5/7), 6-2, 6-3 in three hours 20 minutes and will play Milos Raonic or Gael Monfils in Friday's semi-final.

Ferrer proved a difficult proposition for Murray, relentlessly slugging it out from the baseline and keeping the Scot working hard in a physically demanding match on Rod Laver Arena.

The Scot, distracted by his father-in-law's collapse earlier in the tournament, reached his 18th Grand Slam semi as he attempts to go one better after losing four of the last six Melbourne finals. 

Murray appeared to benefit in the change to the slower court conditions when the roof was closed on Rod Laver Arena in the third set because of an approaching thunderstorm.

"I found it a bit easier to return. It was quite windy when the roof was open, so returning was tricky and against David's extremely accurate forehand that helped me a little bit," Murray said.

"It was actually good for us to have a little break because we played some brutal rallies at the beginning of the third set and also at the end of the second so I came back a bit more refreshed."

Murray, who has noticeably quickened his previously weaker second serve, extended his record over Ferrer to 13-6.

The tenacious Spaniard made 17 errors on the way to dropping the opening set in 45 minutes, following a service break in the fourth game.

It was titanic second-set struggle with Murray double-faulting on break point to go 0-2 down, before breaking back in the seventh game when Ferrer's forehand was well out.

Ferrer had the better of the tiebreak, winning one memorable rally that stretched to 31 shots, and clinched it on his first set point when Murray's forehand was wide.

Murray got a crucial early break in the third set before play was temporarily delayed by the closure of the stadium roof.

The world number two pressed and looked better suited by the slower court speed in the indoor conditions as he broke Ferrer again in the eighth game to take a two sets to one lead.

Murray grabbed another break early in the fourth set when Ferrer's running backhand crosscourt was just wide.

He handed back the break in the next game but then broke Ferrer in the sixth and went on to take it on his first match point, with a wide serve forcing Ferrer's return out.