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Monfils, the French number one who is ranked 12th in the world, displayed none of the nerves he feared would emerge in the opening rubber of France's campaign for a 10th crown.
In spite of a cold, the 24-year-old Parisian instead displayed composure in front of the largely partisan crowd as he sailed through the first set, handled a more determined charge from Tipsarevic in the second and dominated the third set as his opponent crumbled.
Tipsarevic, who was Serbia's hero in the semi-final defeat of the Czech Republic, was on occasion subject to jeers and whistles from some sections of the crowd in the final set as it became clear his challenge would soon fizzle out.
Serbia, however, has been looking forward to this event for weeks and is determined to seize their opportunity to win their maiden Davis Cup crown.
France face a tougher challenge in Friday's second rubber, with world number three Novak Djokovic set to test the resolve of Gilles Simon.
Simon, ranked 42 in the world, has beaten Djokovic only once in their six previous meetings although France captain Guy Forget is hoping the hard indoor surface at the Belgrade Arena will suit his style of play.
Michael Llodra and Arnaud Clement will represent France in Saturday's doubles encounter when they meet Nenad Zimonjic and Viktor Troicki.
Llodra remains an option for France in the event he is needed for one of the two reverse singles matches on Sunday.
Both team captains have the choice of changing their doubles line-up up to one hour before the start of the match. The same rules applies to Sunday's reverse singles but does not apply to Friday's matches.
