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To add tragedy to loss, a 24-year-old River fan fell about 18 metres to his death in a car park behind one of the stands at the Velez Sarsfield stadium during Monday night's match.
Godoy Cruz midfielder Nicolas Olmedo scored the winner at Velez, where River were the home side due to a ban on their own Monumental stadium following hooligan violence.
River, who last won the title in 2004, have played poorly all season under coach Daniel Passarella to a backdrop of infighting at the club where factions of rival "barrabrava" hooligan fans have been locked in a power struggle.
They were eliminated from the Libertadores Cup, South America's champions league which they have won twice, in the first round and are 10 points off the pace in the Clausura with only six points left in play.
San Lorenzo are top with 39 points, four more than Boca Juniors and six in front of Apertura champions Estudiantes de La Plata, and could lift the title this weekend with a game to spare when they host fourth-placed Arsenal.
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