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,” Murray said.
“I would have been very disappointed if I’d lost the second set, but also, I didn’t feel like I was playing badly.
The Scot held off Kohlschreiber’s match points, but still needed eight set points to take the contest into a decisive final set.
Thursday’s dramatic second set equalled five other 20-18 tiebreaks recorded since tiebreak scores were first kept in 1991.
“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,” Murray said.
“I’ve have been playing on the tour for 11, 12 years now, and nothing’s been close to that.”
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.
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.
