Boca, who clinched the title last weekend, lost 3-1 away to Rosario Central who finished third but also go into South America's top club competition as runners-up to Boca in the Copa Argentina.
Boca have 64 points from 30 matches, three more points than San Lorenzo with Central five behind and Racing Club seven adrift.
Striker Nicolas Blandi scored for San Lorenzo, Libertadores winners in 2014, who were a man short from the 22nd minute when defender Fabricio Fontanini was sent off for a second booking.
Rafaela midfielder Walter Serrano was sent off in the final minutes.
In a tense atmosphere at Rosario, a huge police operation involving 900 officers ensured there was no fan violence as Central gained a measure of revenge for their controversial defeat by Boca in the Copa Argentina final in midweek.
Central's players were angered with the referee for awarding a penalty for a foul that occurred outside the box and a goal scored from an offside position in Wednesday's final of the knockout competition.
The referee and his linesman, who on seeing replays later admitted their mistakes, have been suspended by the Argentine FA.
Striker Andres Chavez put Boca, who fielded a number of reserves, ahead in the ninth minute on Sunday.
Central turned the match around in the last half hour with former Olympique Lyonnais and Argentina striker Cesar Delgado scoring the equaliser in the 63rd minute.
The division's top scorer Marco Ruben failed to get among the Central scorers and finished with a tally of 21.
River Plate, who go into the 2016 Libertadores Cup as holders and play the Club World Cup in Japan next month, fielded a side full of reserves at home to Newell's Old Boys and lost 2-0, finishing 15 points behind arch-rivals Boca.
Their form has dipped badly since August with only three wins in their last 12 league matches in which they have scored 10 goals, four of them in one game.
(Writing by Rex Gowar; Editing by Greg Stutchbury)
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