Murray returns the ball to Kohlschreiber on March 2, 2017. PHOTO: AFP
The top seed managed to avoid joining second seed Stan Wawrinka and seven-time winner Roger Federer on the sidelines after the Swiss pair crashed out in earlier rounds.
But world number one Murray needed to scrap and struggle for almost three hours against 33-year-old Kohlschreiber, with the pair duelling in a 31-minute second-set tiebreaker which determined the final direction of the epic quarter-final.
"It was very rewarding to come through a match like that and obviously I'm very pleased to get through it," said Murray.
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"I would have been very disappointed if I'd lost the second set, but also, I didn't feel like I was playing badly.
"I played a poor tiebreak in the first set, but apart from that, I felt I was playing pretty well and he was playing really good stuff," he added.
The Scot held off Kohlschreiber's match points, but still needed eight set points to take the contest into a decisive final set.
The result ended Kohlschreiber's quest for a 400th match win.
Thursday's dramatic second set equalled five other 20-18 tiebreaks recorded since tiebreak scores were first kept in 1991.
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Such was the drama that Murray and Kohlschreiber forgot to change ends at 15/15, instead changing at 16/16.
"I've never played a tiebreak that long ever. Not in juniors, nothing even close to that, I'll probably never play another one like that again," said Murray. "I've have been playing on the tour for 11, 12 years now, and nothing's been close to that."
Murray will next meet French seventh seed Lucas Pouille who defeated Russian qualifier Evgeny Donskoy, the man who stunned Federer, 6-4, 5-7, 7-6 (7/2).
Pouille, who has lost all three matches he has played against Murray, completed his quarter-final win at 1.46 on Friday morning in Dubai.
Murray has never won the Dubai title, but came close in 2012 when he was runner-up to Federer.
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In the bottom half of the draw, fourth seed Gael Monfils fired 10 aces but still crashed out 6-3, 7-5 to Fernando Verdasco.
The French showman was unable to make a major impression in a match which was paused for almost half an hour in the closing stages due to light rain.
Spain's Verdasco will play his second semi-final of the season on Friday, facing Dutchman Robin Haase, a 6-2, 4-6, 6-4 winner over Bosnian Damir Dzumhur.
Monfils lost for the first time in four meetings against Verdasco, with the unseeded Spaniard taking charge from the start.
Verdasco spent 35 minutes in winning the opening set and set about consolidating in the second.
The 33-year-old, ranked 35th, broke for 3-2 with Monfils saving three break points in the seventh game to stay in touch.
But Verdasco then produced a love game for 5-3 just before rain stopped play. The Spaniard finally prevailed after 81 minutes.
"I played almost a perfect match," said Verdasco. "I'm very happy, it was a really complete match in all the ways that you can imagine."
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