The young Costa Rican side, with only about half the senior squad that played at last month's CONCACAF Gold Cup in the United States, climbed to second in the group with three points, one ahead of Argentina and one behind leaders Colombia.
A disappointing Argentina have dropped points to Bolivia and Colombia, who drew 0-0 with the hosts in Santa Fe on Wednesday after beating Costa Rica 1-0 on Saturday.
Bolivia had defender Ronald Rivero and midfielder Walter Flores sent off in the final 19 minutes.
"In the second half I pulled Campbell over to the left wing where he was able to make a difference and his confidence grew," Costa Rica's Argentine coach Ricardo La Volpe told the post-match news conference.
"After Argentina's result last night, this result today doesn't make things any easier for them."
Striker Josue Martinez put Costa Rica ahead on the hour when he netted the rebound after Bolivia goalkeeper Carlos Arias parried a shot from Allen Guevara.
The 19-year-old Campbell made it two in the 79th shooting from the left under the advancing Arias.
PENALTY MISS
Guevara could have put Costa Rica two up earlier with a 72nd-minute penalty but Arias saved his spot-kick and also the midfielder's second attempt from the rebound.
The penalty had been awarded for handball by Rivero, who was sent off after blocking a goal-bound shot from Heiner Mora with his arm.
Bolivia then had Flores shown the red card in the 76th for a blatant foul on Campbell as he dribbled his way towards the box. Midfielder David Guzman hit the near post from the resulting free-kick.
Bolivia striker Marcelo Martins missed two chances in the first half when the Bolivians held the initiative.
First Martins was just too late to a low cross by Juan Carlos Arce and later he mis-kicked another cross following a good attacking move.
Costa Rica came very close in between when defender Pedro Leal crossed and Martinez's header was on target but went out for a corner off defender Ronald Raldes.
Minutes after the first goal, Martins could have equalised but failed to get a touch to a shot from Edivaldo Rojas that went out close to the post and later Campbell hit the bar after a free-kick.
