Young midfielder Juan Sanchez Mino, playing for rested captain Juan Roman Riquelme, opened the scoring in the 59th minute with a low shot from the edge of the box and substitute Pablo Mouche added the second three minutes from time.
After four matches, Boca, who have yet to concede a goal, have 10 points, two more than Velez Sarsfield, Estudiantes and All Boys. Tigre joined Boca on 10 points with a 1-0 home win over Lanus.
"This was a very important win to ratify what we did [in winning the Apertura championship]. We have an important match for the Libertadores Cup at home on Wednesday which we must win," Mouche told Futbol Para Todos.
Boca meet Brazil's Fluminense in Group Four.
San Lorenzo remain mired in the bottom four of the parallel relegation standings which are calculated on teams' average points over three seasons. They occupy a playoff berth, like fellow big club River Plate who lost it last June and were relegated.
The Saints' behaviour in added-time hardly reflected their nickname as Gabriel Mendez was sent off for a two-footed lunge on fellow substitute Diego Rivero.
Uruguayan striker Carlos Bueno and Boca defender Juan Insaurralde were also shown the red card by referee Sergio Pezotta for fighting.
Boca might have gone ahead in the first half at San Lorenzo's Nuevo Gasometro ground but goalkeeper Nereo Champagne saved brilliantly from striker Dario Cvitanich and Insaurralde put striker Santiago Silva's low left cross wide.
Uruguayans Juan Manuel Salgueiro and Bueno had second-half chances for the home team but both were guilty of misses with Boca goalkeeper Agustin Orion at their mercy.
Racing Club picked up only their second point of the championship with a 0-0 draw at Arsenal to keep the wolves at bay after two successive defeats shocked fans expecting a good championship under popular coach Alfio Basile.
Their only consolation is that fellow giants and Avellaneda neighbours Independiente have lost all four of their matches. Their coach Ramon Diaz resigned on Saturday night after they went down 3-1 at home to Argentinos Juniors.
Tigre, despite their lofty position at second in this championship, are in even greater danger of relegation than San Lorenzo, though their good form could help steer them clear.
They are one from bottom of the relegation table and the last two in June will go down automatically.
