Midfielder Sebastian Blanco put San Lorenzo ahead in the ninth minute of the match in La Plata with his first goal for the club since arriving last year.
Barrientos then made sure of the victory midway through the second half.
The former Catania midfielder executed a superb lob from just inside the halfway line that had goalkeeper Agustin Silva scurrying back frantically from the penalty spot in a futile attempt to stop the ball going in under the bar.
“That was probably my best goal ... Luckily the ball went in behind the goalkeeper,” the substitute said.
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It was a timely win for San Lorenzo after home defeats by modest San Juan in the league and Corinthians of Brazil in the Libertadores Cup, though it came against an Estudiantes side made up largely of reserves due to injuries.
Estudiantes were also giving some players a rest ahead of their Libertadores Cup visit to Libertad in Paraguay on Thursday.
At the top of the table, Central have a maximum 12 points after Saturday’s 3-1 win at Olimpo, the highlight a hat-trick by striker Marco Ruben.
Boca Juniors are two points behind after Sunday’s 1-1 draw at Colon in Santa Fe where substitute Dani Osvaldo missed three good chances to give his new team the three points.
“We left the pitch angry at the result, not our game," Osvaldo’s striker partner Jonathan Calleri told Fox Sports on Monday. "We must improve our finishing ... It was our best match of the championship.”
South American champions San Lorenzo and Estudiantes both have nine points.
(Editing by Peter Rutherford)
