Murray stuns Tsitsipas to reach Stuttgart semi-finals
Stay tunned with 24 News HD Android App
Murray, making his debut at the German venue, will wait for a Saturday opponent as Nick Kyrgios faces Hungarian Marton Fucsovics in the day's last quarter-final.
"It was an amazing atmosphere," 35-year-old Murray said in his on-court interview after securing a first top five win since 2016.
"Almost full crowd. Beautiful weather today, really nice conditions to play tennis. I thought I did well. He served unbelievably in the first set.
"I felt like I had very few chances, but when he was creating chances on my serve, I stayed strong. I played a really solid tie-break and in the second set, once I was in the rallies, I felt like I was dictating a lot of the points. It was a good performance."
World number five Tsitsipas saved two match points in the penultimate game, with the Scot finishing off victory a game later with a winner down the line on his third chance.