Djokovic silences Britain, helps Serbia into Davis Cup semis
The 36-year-old rebuked British fans at the end of the match as they tried to down out his victory speech.
After Miomir Kecmanovic edged Jack Draper 7-6 (7/2), 7-6 (8/6) in the opening clash 24-time Grand Slam winner Djokovic outclassed a stubborn Norrie to book a date with Jannik Sinner's Italy on Saturday, after they beat the Netherlands 2-1.
Djokovic, who beat Sinner to win the ATP Finals on Sunday in Turin before flying to the Costa del Sol, celebrated his landmark 400th week at number one with a straight sets win over Norrie, the captains agreeing not to play the redundant doubles.
British fans outnumbered Serbs at the sold-out Martin Carpena arena but the relentless Djokovic silenced them with his 21st consecutive Davis Cup singles win.
"Keep going, keep going," said Djokovic, addressing British fans trying to drown him out with drums as he spoke after his win.
"Learn how to respect people, learn how to respect players, learn how to behave yourselves."
Djokovic said earlier this week winning the competition is one of his "greatest goals" in a year where he has lifted seven titles, including three Grand Slams.
The veteran star was part of Serbia's only Davis Cup triumph in 2010 and his country eliminated 10-time champions Britain, who faced an uphill struggle after Kecmanovic defeated Draper in two tie-breaks.
Britain, without the injured Andy Murray and Dan Evans, were hoping Draper could give them a cushion.
Serbia captain Viktor Troicki selected Kecmanovic over the higher ranked Laslo Djere and the world number 55 raised his game in return.
Draper staved off two set points to hold for 5-5 but unravelled in the first tie-break, double faulting twice and miscalculating a drop shot to hand the Serbian the set on a plate.
After composing himself the second set was even tighter than the first, with neither player able to find a break again.
The near-flawless Kecmanovic triumphed when Draper lashed a forehand wide and then pushed a return into the net.
"It was definitely very close, and just the atmosphere made it, I think, even more tense than it probably would be if it was like an ATP match or something," said the Serb.
Sealed with a kiss
Djokovic set out with his mission clearly defined and earned two break points at 2-2 and took the second of them to nose ahead with a well-judged touch over the net which the scrambling Norrie just failed to reach.
The Briton was pulled to-and-fro by Djokovic but scrapped to survive four break points for an extremely tough hold from love 40 down, to trail 4-3. One superb overhead earned Norrie applause from Djokovic.
The 36-year-old offered little else after that to his opponent though and closed out the first set serving to love with a volley, before cupping his ear and blowing sarcastic kisses to a couple of British fans who had upset him.
Djokovic broke to love in the first game of the second set as he began to hit his stride and show off his lethal forearm.
British No 1 Norrie, 18th in the world, showed resilience but never came close to finding a way back into the match.
Djokovic served it out, finishing with an ace.
On Friday, last year's runners-up Australia face surprise package Finland in the first semi-final.