Thiem beat the 32-year-old 6-2, 3-6, 7-5, 5-7, 7-5 in the semifinal, which began on Friday but was interrupted by bad weather three times, BBC Sport reported.
The fourth seed will face 11-time champion Rafael Nadal today, a repeat of last year's final.
Thiem, 25, is the first Austrian player to reach a second Grand Slam final.
"It was an unbelievable day for me," said Thiem, who had never beaten a world number one at a major before.
Friday's play was suspended once, then cancelled because of wind and rain in a move criticized by former players and journalists, who pointed out that the skies later cleared with daylight still left.
Nadal's semifinal win over Roger Federer took place earlier on Friday so was not affected by the suspension, while Thiem wrapped up victory on Saturday afternoon after the third break in play because of rain.
Djokovic had won 26 Grand Slam matches in a row and was aiming to be the first man in the Open era to hold all four major titles at once on two separate occasions.