The defending champion earned only one opportunity to break serve in the opening set against the Uzbekistan player, but grabbed it ruthlessly to seize control of the match in the Pat Rafter Arena.
Istomin, ranked at number 43 in the world, failed to capitalise on two break points on the Murray serve, but continued to battle through the second set as he pushed his opponent to a tie-break, which the world number three won for the loss of three points.
Though Istomin opened up a 2-0 lead with an early mini-break, Murray won seven of the next eight points to wrap up the match in 97 minutes and win through to the last four of the Australian Open warm-up event he won last year.
The US Open champion struggled in his opening three-set win against John Millman on Thursday, but looked more comfortable in his second match of the year against his 26-year-old opponent.
"For the most part it was pretty good quality," said Murray. "He served well for the majority of the first set, and especially well at the beginning the second. So I didn't really have that many chances on returns, so I needed to serve well today. That helped."
Murray, who reached the semi-finals of the Australian Open in 2012, is continuing his warm-up for the first Grand Slam of the year in Melbourne, which gets under way on January 14.
He will next take on fifth seed Kei Nishikori of Japan looking for a place in his 38th tour-level final, with the Japanese player having beaten fourth seeded Ukrainian Alexandr Dolgopolov of Ukraine 6-4 7-6 (7-3).
When asked about facing Nishikori in the last four, Murray added: "It will be a very tough match, because he is very quick."
Gilles Simon was the highest profile casualty on a day which saw a number of seeded players sent packing from the ATP tournament after he was ousted by Marcos Baghdatis 6-3 6-4 in the first of the day's quarter-finals at the Queensland Tennis Centre.
Cypriot Baghdatis won 78 per cent of his first serves and broke the French third seed three times on his way to what was a comfortable victory. He now plays Grigor Dimitrov for a place in the final, after the Bulgarian toppled seventh seed Juergen Melzer 6-3 6-2 in another upset.
Dimitrov fired down 17 aces, winning 84 per cent of his first serves and taking all four of the break points he had in a match that lasted just under an hour.
In Doha, Nikolay Davydenko continued his superb week by beating top seed David Ferrer 6-2 6-3 in the semi-finals.
Davydenko went into the event unseeded but is now just one match away from winning for the second time in Doha after his triumph in 2010.
He will face second seeded Frenchman Richard Gasquet in the final who saved all three break points he faced in a 7-5 7-5 victory over Germany's Daniel Brands.
ATP Brisbane results
1-Andy Murray (Britain) beat Denis Istomin (Uzbekistan) 6-4 7-6(3)
5-Kei Nishikori (Japan) beat 4-Alexandr Dolgopolov (Ukraine) 6-4 7-6(3)
Grigor Dimitrov (Bulgaria) beat 7-Jurgen Melzer (Austria) 6-3 6-2
Marcos Baghdatis (Cyprus) beat 3-Gilles Simon (France) 6-3 6-4
ATP Chennai results
Roberto Bautista (Spain) beat 1-Tomas Berdych (Czech Republic) 7-5 2-6 6-3
2-Janko Tipsarevic (Serbia) beat 8-Go Soeda (Japan) 6-2 6-4
Aljaz Bedene (Slovenia) beat 4-Stanislas Wawrinka (Switzerland) 6-2 7-6(6)
5-Benoit Paire (France) beat 3-Marin Cilic (Croatia) 6-4 1-6 7-5
ATP Doha resutls
2-Richard Gasquet (France) beat Daniel Brands (Germany) 7-5 7-5
Nikolay Davydenko (Russia) beat 1-David Ferrer (Spain) 6-2 6-3