Third seed Wawrinka, the current US Open champion, had his work cut out against the dangerous Thiem but managed to claim the opening set at the Indian Wells Tennis Garden.

But Thiem hit back as he began to find his range on his way to levelling the match at one-set all.

That left the fascinating contest on a knife-edge and the drama was intensified when the decider went to a tie-break, which Wawrinka was able to dominate as he wrapped up a 6-4, 4-6, 7-6 win. 

The 31-year-old Swiss will take on Spain's Pablo Carreno Busta, seeded 21st, in his first-ever Indian Wells semi-final.

Carreno Busta also needed three sets to get past his quarter-final opponent as he saved two match points in his 6-1, 3-6, 7-6 triumph.

"The level was really high tonight," Wawrinka said.

"I'm really happy the way I was playing, the way I found a way to win it.

"The player who was the most aggressive, was dictating, was winning most of the points.

"I'm really happy to have served well in the tiebreak. 

"I think that was the key."

In the women's singles, France's Kristina Mladenovic broke into the world's top 20 as she fought back from a set down to overcome Denmark's Caroline Wozniacki.

The Dane, a former world number one who was victorious at this event in 2011, started the better of the two players before Mladenovic clawed her way back into the match.

The 28th seed started to dominate from the back of the court in the second and third sets and reeled off a series of impressive winners in a 3-6, 7-6, 6-2 success.

Russia's Elena Vesnina awaits in the last four after she beat American Venus Williams 6-2, 4-6, 6-3.