World number two Djokovic and his 2010 Davis Cup champions Serbia team had already booked their place in September's semi-final against nine-time winners France by beating Spain who were hamstrung by the absence of Rafael Nadal.
Djokovic missed the Masters series event with an elbow injury and, having recovered, is eager to face Spain in the Davis Cup quarterfinals in front of a boisterous home crowd in Belgrade this weekend.
Serbia's Novak Djokovic showed glimpses of his best form with a 6-3 6-4 6-2 win over Albert Ramos-Vinolas as they took a 2-0 lead over Spain in the Davis Cup quarter-finals yesterday.
Viktor Troicki followed up by doubling the advantage in a three-set victory of his own, 6-3 6-4 6-3 over Pablo Carreno Busta.
Serbia, Australia, France and Belgium all took 2-0 leads to take control of their respective ties on day one of the Davis Cup quarter-finals.
But it didn't happen and the Serbian player won in straight sets.
"He's had his ups and downs in the last three or four years but came back swinging and revitalized after a six-month layoff last year", Djokovic said.
"We must not underestimate them", Djokovic said.
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"I personally always draw very positive energy from these weeks", said Djokovic, whose career went into warp drive after helping Serbia win the 2010 Davis Cup title.
"It worked well today and I won a lot of points off my first serve".
France are unable to call on the services of their top two players, Jo-Wilfried Tsonga and Gael Monfils, although they do feature world number 17 Lucas Pouille in their line-up.
But firebrand Kyrgios needed to seal the deal for Australia on Sunday, securing the winning point in the first of the reverse singles to defeat 32-time champions United States. The Spaniard was on the back foot throughout the match and Troicki won comfortably in one hour 48 minutes.
British pair Dominic Inglot and Jamie Murray gave up breaks when serving to remain in the third set and match, Benneteau and Mahut running out 7-6 (9-7) 5-7 7-5 7-5 winners to keep their nation's hopes of a first title since 2001 alive.
"I'm very happy", said Bolelli.
Great Britain, the team who beat the Belgians to the 2015 title, head to the Kindarena in Rouen for their match with France.