Djokovic missed the Masters series event with an elbow injury and, having recovered, is eager to face Spain in the Davis Cup quarter-finals in front of a boisterous home crowd next weekend.
Viktor Troicki, the world 39, then made it 2-0 for Serbia by seeing off 19th-ranked Pablo Carreno Busta 6-3, 6-4, 6-3.
The win in the doubles followed Lucas Pouille and Jeremy Chardy taking the opening singles on Friday as Britain suffered in the injury-enforced absence of world number one Andy Murray.
Novak Djokovic says playing against Spain in the Davis Cup quarterfinals could boost his form ahead of his return to competition.
On the indoor hard court of the Aleksandar Nikolic Arena, Spain will be led by world No19 Pablo Carreno Busta, who is his nation's No3 behind the absent Nadal and Roberto Bautista Agut.
According to serbian Media, she had said that they would have hoped to beat Troicki in both singles match in order to win two points because Victor wasn't good enough, but that's not correct.
It was veteran Zimonjic's 30th Davis Cup doubles win.
However, the identity of the other semi-finalists will not be known until Sunday after the United States pulled back to 2-1 down against Australia in Brisbane while Italy battled to trail Belgium 2-1 at Charleroi. "I'm trying to knuckle down and compete for every point and that's something I haven't done in the past", said Kyrgios.
With the USA boasting a team of in-form Jack Sock, John Isner, Sam Querrey and Steve Johnson, Hewitt will be banking on two wins from the mercurial Kyrgios as his second singles player is the inexperienced world number 79 Jordan Thompson.
"I skipped Miami and I haven't done much in Indian Wells, so the start of the season wasn't ideal, " Djokovic said. His only loss during that stretch was against Andy Murray in the 2015 final.
Belgium, the only won of the quarter-finalists never to have lifted the trophy stunned Germany in Frankfurt without David Goffin in round one but will have their top player back for the home clash with Italy in Charleroi.