Red Star's fourth successive opening day defeat piled the pressure on their Slovenian coach Slavisa Stojanovic after they were also eliminated by Ukrainians Chernomorets Odessa in the Europa League third qualifying round on Thursday.
"We were absolutely dreadful and devoid of any creativity, all I can do is congratulate the hosts for their well-deserved win," a dejected Stojanovic told Serbia's Arenasport television.
Javor coach Bogic Bogicevic said: "We let in two soft goals after a perfect start but the lads were magnificent in the second half and only some very good saves by (Red Star goalkeeper Boban) Bajkovic denied us a bigger win."
Javor raced into an early 2-0 lead through Milovan Milovicand Nigerian striker Ifeanyi Onyilo at their ramshackle ground, but Red Star were level before the half hour through Filip Kasalica and Nejc Pecnik.
Red Star took control until central defender Novak Martinovic was sent off for a second yellow card midway through the second half after he hauled down the pacy Onyilo.
Pedrag Djordjevic headed in a corner at the near post in the82nd minute and, with Red Star throwing caution to the wind in search of an equaliser, Stefan Drazic broke away on the right flank and beat Bajkovic with a crisp shot.