The Serb won 6-7 (6/8), 6-2, 7-5, 6-4 against Flavio Cobolli in front of Britain’s Queen Camilla to reach the Wimbledon last four for a record 14th time in the men’s game.
Earlier, three-time major champion Sinner eased pre-match injury fears to sweep past US 10th seed Ben Shelton 7-6 (7/2), 6-4, 6-4 in an impressive display.
In the women’s draw, five-time Grand Slam winner Iga Swiatek and former Olympic champion Belinda Bencic both reached the semi-finals for the first time and will clash for a place in the final.
Seven-time champion Djokovic was pushed hard by Italian 22nd seed Cobolli but ultimately had too much nous and craft for the 23-year-old.
“It means the world to me that I’m still able at 38 to play the final stages of Wimbledon,” he said on court. “Thank you for cheering for my age. I really appreciate it. It’s beautiful. Makes me feel very young.”
“And I guess another thing that makes me feel very young is competing with youngsters like Cobolli today,” he added.
Djokovic is now within two wins of breaking his tie with Margaret Court for the most Grand Slam singles titles for any player, man or woman.
But Sinner will offer a different level of challenge.
The top seed has won his past four matches against Djokovic, beating him in straight sets in the semi-finals of the recent French Open.
Sinner had sparked fears he may have to pull out of the tournament after falling early in his fourth-round tie against Grigor Dimitrov on Monday.
He was trailing by two sets and on the brink of a shock exit when the Bulgarian pulled a pectoral muscle while serving and had to retire.
Sinner wore a protective sleeve on his right arm against Shelton and said his injury had “improved a lot” after his practice was curtailed on Tuesday.
Carlos Alcaraz, who has beaten Djokovic in the past two finals at Wimbledon, takes on US fifth seed Taylor Fritz in Friday’s other semi-final. (AFP)