The Argentine side had held a comfortable 5-0 advantage from last week's first leg and sat back to defend in two lines of four, 3,600 metres up on Bolivia's Andean plateau.
Substitute Gerardo Yecerotte scored the only goal for Bolivar in the second minute of added time on a poor Hernando Siles pitch.
San Lorenzo will meet Nacional of Paraguay, also first time finalists after beating Uruguay's Defensor Sporting 2-1 on aggregate on Tuesday, over two legs for the South American club title and a place in the Club World Cup in December.
"We made a great effort, we've got one more step to fulfil our dream of winning the Cup," playmaker Leandro Romagnoli said.
"We weren't able to play (Bolivar) as equals because of the matter of the altitude and that annoys us, but we achieved our objective," he told Fox Sports.
The match was preceded by a minute's silence in memory of Argentine FA president Julio Grondona who died earlier in the day aged 82.
Bolivar made a whirlwind start as they embarked on the near impossible task of levelling the tie after last week's crushing 5-0 defeat at the Nuevo Gasometro.
Colombia striker Carlos Tenorio skimmed the outside of the post with an early shot and midfielder Jose Luis Capdevila hit the bar a minute later.
San Lorenzo, trying to pace themselves and conserve energy, won a corner after 11 minutes with striker Nicolas Blandi then forcing goalkeeper Romel Quinonez into a difficult save.
Bolivar striker Juanmi Callejon came close with a chance after half an hour and in the 37th minute San Lorenzo midfielder Ignacio Piatti was foiled at the other end when Quinonez tipped his shot over the bar.
San Lorenzo's players then had to be shielded by riot police as they left the field at halftime when a group of Bolivar fans hurled objects at them.
Bolivar wasted good chances for striker Juan Arce and defender Ronald Eguino in the second half as San Lorenzo sat deep in their own half.
The Argentine side's defence was finally breached in Bolivar's last attack when a shot by Tenorio came back off a defender and Yecerotte slotted past Sebastian Torrico.
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- Gerardo Yecerotte