Shelton had flummoxed opponents in New York with his big serve but the second seed Djokovic was able to harness his experience to neutralise a third-set surge from the young American.
He next faces the winner of a match between top seed and defending champion Carlos Alcaraz (20) and third seed Daniil Medvedev (27).
"Obviously I knew that he's got a lot of firepower. He has an amazing pop on the serve, he's just so dynamic and very unpredictable what comes next," said Djokovic. "I just had to stay there mentally, present, calm, and focus on the game plan."
Already assured of returning to the top of the world rankings when they are updated after the tournament, Djokovic will continue the hunt for his 24th Grand Slam title to match Margaret Court's all-time singles record on Sunday.
Shelton handed Djokovic a break in the sixth game of the first set with a series of unforced errors, and the unseeded American was unable to convert his own break point chance in the ninth.
In the second set, Shelton's best weapon failed him as he helped Djokovic secure a break with a double fault in the fifth game and he dropped his racquet in frustration as he sent a forehand out to hand the Serb another break in the seventh.
Djokovic was competing in his 47th major semi-final while Shelton was appearing in his first. The difference in experience was apparent as the second seed broke Shelton with a fine forehand winner in the opening game of the third set.
But the American came to life late as he fended off a break point with a 143-mph (230-kph) ace in the fifth game to a chorus of cheers from the home crowd.
Playing in only his seventh US Open singles match, Shelton triumphed in a 30-shot rally before converting a break point in the eighth game, humbling Djokovic, who was appearing in his 100th singles match at the hardcourt major.
Djokovic broke again in the 11th game but could not stop the set from going into a tiebreak as he swatted one into the net to allow Shelton to break back in the 12th game.
The Serb forced Shelton into a forehand error on match point and made a not-so-subtle jab at the American's favoured celebration as he mimed answering - and hanging up - the telephone while walking to the net.
"I just love Ben's celebration," Djokovic told reporters with a grin.
"I thought it was very original, and I copied him. I stole his celebration."
Shelton said he had not seen Djokovic's move until after the match - but added that he would not tell another opponent how to celebrate.
"I think if you win the match, you deserve to do whatever you want," said Shelton.
"You know, as a kid growing up, I always learned that imitation is the sincerest form of flattery, so that's all I have to say about that."
Speaking about how it could be his ultimate final, Djokovic said: "At 36, every Grand Slam final, yeah, I don't know, could be the last one,"
"I probably value these occasions and opportunities to win another slam as more than I have maybe 10 years ago, because 10 years ago I felt like, 'Hey, I still have quite a few years ahead of me'. I don't know how many I have ahead of me now."
Shelton said he was taking lessons away from the tournament in what he can achieve.
"I learned a lot about myself these two weeks, knowing how, you know, deep I can go, how deep I can dig," said Shelton.
"I kind of found a place where I can operate and still be calm and still be clear-minded but be a fierce competitor."
The match was played under increased security after an incident on Thursday night, in which a protester glued his feet to the floor of Arthur Ashe Stadium, forcing a nearly one-hour stoppage of a semi-final match between American Coco Gauff and Czech Karolina Muchova.
