Djokovic is bidding for a record-equalling sixth title at the season-ending tournament but has not lifted the trophy since 2015.
He arrived in Italy on the back of a 37th Masters title in Paris and kept his winning run going with a 7-6(4) 6-2 victory over Ruud, who is the first Norwegian to qualify for the tournament.
Djokovic dropped serve in the opening game after a point when he stumbled and dropped his racket before netting, but he settled into the match and broke back for 3-3.
Ruud, who has developed his game this year to be a threat on all surfaces, rather than just his favoured clay, did well to save two set points at 4-5, but Djokovic came out on top in the tie-break.
The second set was a masterclass from Djokovic, who applied intense pressure to his 22-year-old opponent’s serve and eased to victory.
Djokovic said: “I don’t know what happened in that break point in the first game. I took a fall, tripped on my own legs a couple of times, so it was really a terrible start, but also funny that I’m still trying to figure out what happened.
“But Casper started strong. He was hitting solid, especially from the forehand side. He was serving very well. Altitudes, fast court, fast balls, it favours big servers.
“The momentum shifted to my side when I managed to have a very strong last three, four points of the tie-breaker, and then I was kind of on the roll and I felt that momentum shifted to my side, and then I was serving extremely well.”
Tsitsipas pulled out of the Paris Masters with an arm injury and was second best against Russian Rublev, who triumphed 6-4 6-4.
The pair have a number of close battles, including at the same tournament in London last year, when 2019 champion Tsitsipas won on a deciding tie-break.
But this contest went the way of Rublev, who produced a brilliant serving display, particularly in the first set, and dictated with his forehand to boost his chances of qualifying for the semi-finals.
Tsitsipas declined to comment on his fitness, but said: “I’m excited. I still want to play good tennis and, despite the loss today, I’m given more chances. I want to step it up and show better tennis next time.”
This is the first time two British doubles players have qualified for the tournament as one of the top eight teams of the year, with Salisbury partnering American Rajeev Ram and Murray teaming up with Brazilian Bruno Soares.
The pairs faced each other in their first group match and, for the third time this year, it was Salisbury and Ram that came out on top.
They had previously met in the semi-finals of the Australian Open and the final of the US Open, and here Salisbury and Ram capitalised on a fast start to win 6-1 7-6(5).
Murray dropped serve twice in the opening set, but the second was much tighter, with both teams missing chances to forge ahead.
Ram and Salisbury took an early lead in the tie-break, though, and a return winner from Ram on their second match point clinched victory for the second seeds.
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