Murray cut a frustrated figure for most of the match, not helped by the resilience of the world number 44, but he regained sufficient composure to break Almagro in the 11th game of the second set and then serve his way into the final four.

Third seed Berdych took considerably less time to secure his progression against Jo-Wilfried Tsonga.

The Czech needed just over an hour and a half to see off the Frenchman 7-5 6-3, and will now look to beat Murray for the first time in seven meetings.

World number two Novak Djokovic will play Fernando Verdasco in the other semi-final after cruising past veteran qualifier Radek Stepanek.

The Serb won 6-3 6-3 against 38-year-old Czech Stepanek, while Spaniard Verdasco also came through in straight sets, defeating Croatian sixth seed Ivo Karlovic 6-2 7-5.

Fourteen-time grand slam winner Rafael Nadal will face top seed Milos Raonic in the last eight of the Brisbane International following an emphatic win over Mischa Zverev.

The Spaniard dropped just 24 points as he sealed a 6-1 6-1 victory over the German inside 56 minutes.

Canadian Raonic also had little trouble progressing, seeing off Argentinian Diego Schwartzman 6-2 6-4.

In the other quarter-final in the top half of the draw, Dominic Thiem will meet Grigor Dimitrov.

Austrian Thiem came through a first-set tie-break to eventually beat Australian Sam Groth 7-6 (7/5) 6-3, while Bulgarian Dimitrov was a 6-2 6-4 victor against Nicolas Mahut.

In the Aircel Chennai Open, British number four Aljaz Bedene secured his quarter-final spot with a three-set win over Martin Klizan.

The Slovenia-born player overcame three tie-breaks against the Slovakian, winning 7-6 (7/3) 6-7 (3/7) 7-6 (7/2) to set up a last-eight meeting with Benoit Paire after the Frenchman beat home favourite Yuki Bhambri 6-3 6-4.

Second seed Roberto Bautista Agut was a comfortable 6-3 6-2 winner against Brazilian Rogerio Dutra Silva and he will face Mikhail Youzhny next following the Russian's 6-1 7-5 triumph over Argentinian Renzo Olivo.