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The seventh seed needed an anaesthetic to play the final.
A Russian-speaking official appeared to accuse him of using an obscenity, while he screamed at the line judge.
The Serb won the quarterfinals, 4-6 6-1 6-4 6-3, to stay on track for his fifth straight title.
The American defeated Ukraine's Lesia Tsurenko 6-1, 6-3 in the fourth round.
The former No. 1 set up a last-four meeting with American Tommy Paul.
In the bottom quarter of the women's draw, 12th seed Belinda Bencic continued her smooth run with a 6-2, 7-5 win over Camila Giorgi.
The Croatian, whose last semifinal appearance at a major was at the 2018 Australian Open when he reached the final, encountered stiff resistance from Rublev but his 33 aces made the difference.
Rublev galloped to an early lead and barely gave his opponent a chance as he closed out the match with a powerful forehand winner for his first win over Djokovic and 11th career title.
He beat Czech qualifier Jiri Vesely 6-3, 6-4 in the final.
Humbert stepped up his Wimbledon preparations by producing a clinical display, winning 85 per cent of his first-serve points and hitting nine aces to extend his perfect record in ATP tour finals to 3-0.
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