The 32-year-old Serb will return to court at midday on Saturday trailing 6-2 3-6 3-1 and with plenty of work to do if he is to get a crack at Rafael Nadal in the final.
World number one Djokovic was aiming to join Rod Laver as the only man in history to possess all four slams on two occasions, but he came unstuck against the intelligent Thiem in a match controversially held over from Friday due to bad weather.
"I congratulate Dominic, he played great, especially in the important moments", said Djokovic.
"When you play in the middle of a hurricane it's hard to play well", Djokovic said.
On the resumption Saturday, Djokovic retrieved the break in the seventh game but slipped behind again in the match when Thiem converted a fourth set point.
Nadal also needed five sets to see off Thiem in the quarter-finals at the US Open previous year.
There was one final twist as Djokovic's 53rd unforced error on a wild forehand set up a third match point which the Austrian gobbled up with his 52nd victor.More news: Banks must pass along full rate cut: Lowe
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"That's what it felt like playing yesterday".
After a second rain delay, organizers suspended play at 6:30 pm local time despite the rain stopping and the sun making an appearance. "I guess they know tennis better". The most recent one came at the Australian Open a year ago when he became only the third player in Grand Slam title match after turning 36, following Rosewall and Anderson.
Thiem leads 4-1 in the fifth.
Factor in the two-day contest with Djokovic, which lasted four hours and 13 minutes overall, and Thiem's chances of preventing Nadal collecting a 12th title this afternoon appear annoyingly slim.
"I'm full of adrenaline, of course, still from today's match, and also I will have that tomorrow", he said. Ultimately Nadal, the 11-time champion, will be happy it's Thiem on the other side of the net instead of Djokovic.
Thiem double-faulted at 5-5 to gift Djokovic another break of serve and this time the Serbian made it stick to take the match into a deciding set.
It looked all over when Thiem got to 40-15 in the next game, but from having two match points he then completely subsided himself, flunking the next four points.
Thiem wasted two match points with quick unforced errors when serving for the victory at 5-3 in the fifth, but he made his third chance count, smacking a forehand victor to break Djokovic in the last game.