After David Checa put The Strongest in front in first-half stoppage time on Wednesday, Bolivar ensured the Clasico Paceno - or La Paz Derby - would end level thanks to Jose Luis Capdevila's 75th-minute strike.
The draw took Bolivar to 34 points, one ahead of second-placed Oriente Petrolero, who already trailed the league leaders on goal difference.
The point was also of benefit for The Strongest (28 points, plus seven goal difference), who rose ahead of San Jose (28, 0) into fourth.
Wilstermann (30 points) remain third.
The draw continued Bolivar's dominance of Bolivia's oldest and most prestigious derby in recent seasons, as they have only lost one of the past seven meetings with The Strongest.