The British number one took on the world number one for the first time in a fitting end to the best year of his career.
His reward for 50 match wins, a maiden ATP title at Indian Wells and a climb to 12th in the world was entry into the Finals as second alternate following injuries to Matteo Berrettini and Stefanos Tsitsipas.
Defeat by Casper Ruud scuppered any chance of progressing to the semi-finals and with Djokovic already through, the round-robin stage ended with a dead rubber.
But if anyone queried five-time winner Djokovic’s motivation he immediately proved them wrong, racing away with the first set in 28 minutes.
Norrie, 26, had his moments; a couple of sizzling passing shots and a break point in the second.
But he was left in no doubt about the gulf in class between Djokovic and those in the chasing pack following a 6-2 6-1 defeat.
Norrie said: “He was obviously very relaxed with already being qualified for the semi-final. He came out very solid. I think I played a couple loose points in the first service game. He relaxed a little bit there.
“I mean, for me, I’ve watched him quite a lot, he was very solid. He gave me nothing really.
“I knew he had a good serve. I didn’t really know it was going to be this good! I think he had a very good serving day. He was very relaxed, even going after the second serve at times.
“For my level, for me to compete with him, there were too many free points, too many easy points in there. I think it comes down a little bit to you’re playing him and you try to overplay at times.
“I don’t know, I mean, he was too good. He was very relaxed. He’s playing amazing. The conditions are perfect for him. Too good for me today.”
Djokovic, who plays Alexander Zverev in the last four, said in his on-court interview: “I tried not to think about tomorrow. It’s not easy to walk onto a court knowing that you already qualified, you know your opponent, you know the schedule.
“But look, I tried to be professional. I respect everyone I play and the crowd want to see a match so I tried to give my best. I played really well and took the tie away from Cameron really.”
Ruud defied the odds to upset Andrey Rublev 2-6 7-5 7-6 (5) and set up a semi-final showdown with Daniil Medvedev.
The 22-year-old world number eight came from a set down to take a deciding-set tie-break and secure a first career victory over Rublev at the fifth attempt, as well as a first win over a top-10 player on a hard court.
The first Norwegian to appear at the Finals, Ruud is now the first Scandinavian to reach the last four since Sweden’s Robin Soderling in 2009.
Earlier Great Britain’s Joe Salisbury made it through to the last four in the doubles.
Salisbury and American partner Rajeev Ram beat Colombian duo Juan Sebastian Cabal and Robert Farah 7-5 2-6 11-9 after a match tie-break in the deciding set.
Salisbury and Ram, the US Open champions, topped their group after three wins from three matches.
Salisbury is the last Brit standing in Turin with Norrie departing and Jamie Murray, alongside Bruno Soares, missing out in the doubles.
“Obviously it’s great that we had three of us here playing, and hopefully we can keep it going and go all the way,” Salisbury told Amazon Prime.
Their victory earned a semi-final showdown with top-seeded Croatians Nikola Mektic and Mate Pavic on Saturday.
Murray and Soares’ campaign ended with a third straight defeat, going down 6-3 7-6 (5) against Nicolas Mahut and Pierre-Hugues Herbert.
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