Djokovic, the former four-time champion, was forced to finish his quarter-final over Juan Martin del Potro earlier in the day after their match was rained off late on Friday.
But the setback seemed only to inspire the 30-year-old Serbian second seed, as he set up what is expected to be a mouthwatering final, and first meeting, with Germany's rising star Alexander Zverev.
"It was my best performance of the year," said Djokovic after his 59-minute win over Thiem who had knocked out Rafael Nadal in the quarter-finals.
"I'm overjoyed and happy with every minute that I spent on the court today, even with Del Potro and also now with Thiem.
"It was a perfect match. Everything that I intended to do, I have done it and even more."
Zverev, 20, became the youngest player in a decade to reach a Masters final when he clinched a gutsy 6-4, 6-7 (5/7), 6-1 win over big-serving American John Isner.
Djokovic was the previous youngest Masters finalist, going all the way to the title in Miami as a 19-year-old in 2007.
Zverev will climb to a new career high in the rankings at number 14 by reaching the final and would break into the top 10 with the title.
"I don't look at these kind of stats, who is the youngest player to have a Masters 1000 title or things like this. I try to play match by match and try to improve," said Zverev, who fired 12 aces and 41 winners past the 32-year-old Isner.
Thiem, beaten to the Madrid Masters title by Nadal last week, avenged his loss by dumping Spain's former seven-time Rome champion out in the quarters on Friday.