Campos popped up with a close-range header on 87 minutes to deny Venezuela a win which would have put them firmly on the road to their first ever appearance at a FIFA World Cup finals after skipper Juan Arango had fired them ahead in the 58th minute.
The result saw Venezuela inch ahead of Chile into fourth place in the South American qualifying standings with 16 points from 12 games. Chile however will reclaim fourth spot if they beat bottom side Paraguay in Asuncion later Friday. Bolivia meanwhile remain in touch, mathematically at least, with ten points from 12 games, five points adrift of fifth place.
The top four sides in South America's nine-team round-robin competition will qualify automatically for next year's finals in Brazil, with the fifth-placed side going into a play-off against their Asian counterpart.
A poor first half saw both sides struggle to get a grip on the contest, with an uneven playing surface hampering Venezuela's passing game. Venezuela had the better chances in the opening period, with Arango forcing a scrambling save from Sergio Galarza in the Bolivian goal with a long-range free-kick that seemed to accelerate as it swerved towards goal.
At the other end Bolivia's best chance came from star striker Marcelo Martins. The Flamengo forward latched onto a speculative long ball and lashed an angled shot goalwards only to be denied by Venezuela keeper Renny Vega at the near post. Venezuela's Richard Blanco then forced a fine save from Galarza on 32 minutes before Gabriel Cichero sent a lob wide moments later.
Bolivia saw appeals for a penalty waved away on 34 minutes when Juan Carlos Arce went down after rounding Vega in the box. But Arce's blatant dive was spotted by referee Patricio Loustau, who promptly booked the Bolivian winger.
The deadlock was broken by Venezuela's captain Arango - making his 116th appearance - when he thundered home a header after a flick-on from Richard Blanco after Cesar Gonzalez's corner. But with the clock ticking down Campos punished poor marking in the Venezuelan area to head home the equaliser.