The 36-year-old world number one, looking to complete a remarkable year by helping his country win the Davis Cup for the second time, outclassed Norrie to become his country's most successful Davis Cup player.
Serbia will face Italy on Saturday after Jannik Sinner inspired his team to a comeback win over the Netherlands, the world number four winning his singles and a decisive doubles .
But world number 55 Kecmanovic produced a brilliant performance to beat Draper 7-6(2) 7-6(6) in a fierce battle.
That never looked likely, however, as Djokovic, who won three of the year's four Grand Slam titles and last week's ATP Finals for a record seventh time, dissected the world number 18.
Earlier, in the Martin Carpena Arena which has seen big crowds for Final Eight, Italy kept alive their hopes of a first Davis Cup title since 1976.
Persons:
deportes Martin, Miomir Kecmanovic, Britain's Jack Draper REUTERS, Violeta Santos Moura, Novak Djokovic, Britain's Cameron Norrie, Norrie, Sinner, Andy Murray, Dan Evans, Jack Draper, Serbia's Miomir, Joe Salisbury, Neal Skupski, Draper, Djokovic, Nenad Zimonjic, Kecmanovic, Martin Carpena, Botic van de Zandschulp, Matteo Arnaldi, Tallon Griekspoor, Lorenzo Sonego, Griekspoor, Wesley Koolhof, Martyn Herman, Ed Osmond
Organizations:
Britain, Palacio, deportes, deportes Martin Carpena, Rights, Davis, Italy, Djokovic, Serbia, Martin, ATP, Thomson
Locations:
Serbia, Malaga, Spain, Rights MALAGA, Netherlands, France, Italy, Dutch, Turin