The British no.1 raised hopes of reaching the final after racing into a first set lead to the delight of the Centre Court crowd, but Djokovic showed all the experience of a man who has won the tournament six times previously as he recovered to claim a 2-6, 6-3, 6-2, 6-1 victory.
Norrie, 26, whose previous best at a Grand Slam was reaching the third round, was bidding to become only the second home player this century after Andy Murray to make a men’s final at SW19.
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Hide AdHe stunned the world number three with a break of serve in the first game of the match.
Djokovic hit straight back but Norrie broke the Serbian twice more to win the opening set 6-2 with a major upset on the cards.
But a loose service game in the second set cost Norrie as Djokovic pounced to move 5-3 ahead.
The 20-time grand slam champion served out the set to level the match after an hour and 11 minutes.
With the temperature on court approaching a hot and sticky 30C, Norrie was broken again by Djokovic in the opening game of the third set.
The 35-year-old, who has not lost a match on Centre Court in nine years, was punishing Norrie’s second serve and secured another break for 4-1 before taking the set 6-2 to lead the match 2-1.
Norrie took a bathroom break at the changeover in a bid to regroup, but he dropped serve once more at the start of the third set with Djokovic now in complete control.
It was a valiant effort from Norrie but he was unable to land a telling blow on the Djokovic serve, and the defending champion went on to win 2-6 6-3 6-2 6-4.
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Hide AdHe will face Australian world number 40 Nick Kyrgios in Sunday’s final.