Jack Draper’s defeat to Miomir Kecmanovic earlier in the day had given the British No.1 a mountain to climb and it proved a challenge too far.
The world No.1 picked up where he left off after dominating the ATP finals earlier this month and largely toyed with Norrie for swathes of his 6-4, 6-4 win.
Canada saw their title defence ended by Finland in a big surprise to kick off the 2023 finals action, before Australia defeated Czechia.
Otto Virtanen and Harri Heliovaara beat Vasek Pospisil and Alexis Galarneau 7-5 6-3 as the Final 8 stage got underway in Malaga on Tuesday.
That was followed by Australia edging out the Czechs 2-1 on Wednesday as Matthew Ebden and Max Purcell got the better of Jiri Lehecka and Adam Pavlasek in the decider.
Having won three of the four Grand Slams to take his tally to 24, with only an epic final defeat by Carlos Alcaraz at Wimbledon denying him a clean sweep, Djokovic continued his stellar 2023 by winning a record-breaking seventh ATP Finals title in Turin on Sunday.
The world No1 now turns his focus to a quarter-final tie against Great Britain on Thursday, with Serbia favourites to win the Davis Cup for the first time since 2010. Cameron Norrie is set to be the British player tasked with beating Djokovic, with Andy Murray ruled out with a shoulder injury.
“I will arrive there with not much rest, but we will try our best,” Djokovic said after his ATP Finals win over Jannik Sinner.
Davis Cup 2023 dates and venue
The Davis Cup Finals began on Tuesday November 21, 2023 and run through to the final on Sunday, November 26.
Malaga is hosting the action, with all matches being played at the Palacio de Deportes Jose María Martín Carpena.
How to watch the Davis Cup 2023
TV channel: The Davis Cup Finals will be shown live on the Tennis Channel, which costs £2.49 a month after a seven-day free trial.
Live stream: The BBC iPlayer and the BBC Sport website (both free with a subscription) will offer live streams of Great Britain's quarter-final tie and all of their subsequent matches should they make it through.
Davis Cup 2023 schedule
All times GMT
Tuesday November 21
Finland bt Canada 2-1
Wednesday November 22
Australia bt Czechia 2-1
Thursday November 23
Italy bt Netherlands 2-1
Serbia bt Great Britain 2-0
Friday November 24
Finland vs Australia
Saturday November 25
Italy vs Great Britain
Sunday November 26
Winner of semi-final 1 vs winner of semi-final 2
Davis Cup 2023 format
Unlike the best-of-five ties in the groups, it is best-of-three at the Davis Cup Finals.
The two singles matches will be played first, with a doubles match then deciding the tie if necessary. All matches are best-of-three sets.
Who was playing for Great Britain?
Great Britain captain Leon Smith had to contend with injury problems ahead of his side's quarter-final tie.
Dan Evans, who shone for Great Britain earlier this year to ensure they booked their place in Malaga, has withdrawn with a calf injury, while Andy Murray is also unavailable.
There had been talk of Murray facing Djokovic for the first time since 2017, but a shoulder injury has ruled the three-time Grand Slam champion out of the tie.
Cameron Norrie and Jack Draper played the two singles matches, with Neal Skupski and Joe Salisbury the doubles pairing. Liam Broady has been called up to replace Murray on the team.
Davis Cup 2023 odds
Odds via Betfair (subject to change).