With Universidad San Martin drawing 1-1 at UTC Cajamarca on Monday, San Simon remain a win away - plus goal difference - from leaving last spot in the standings but Jose Carlos Amaral's men at least got on the winner's list on the weekend.
San Simon won 2-0 at Los Caimanes to move to four points for the season from nine matches, ending a four-game losing streak.
Both sides forced their opposing goalkeepers into a number of saves in the first half at the Estadio Elias Aguirre on Sunday, but it was the visitors who opened the scoring after the break.
A free-kick floated forward by Gustavo Stagnaro was flicked into the net by the head of Matias Sen in the 75th minute.
Cesar Mayuri wrapped up the three points for San Simon nine minutes later, tucking away a one-on-one chance, although the 22-year-old midfielder appeared offside.
Universidad San Martin (seven points) remain ahead of San Simon in 15th position, while Cajamarca (eight) and Los Caimanes (nine) complete the bottom four clubs in the table.
At the other end, Alianza Lima (21 points) won 1-0 at Sport Huancayo to stay top, while Sporting Cristal (17), who have a game in hand, thrashed Cesar Vallejo 4-1 to move into second.
Alianza have won six and drawn three of their nine league matches so far this season and were on their way to their latest victory when Gabriel Costa scored in the 34th minute.
Maximiliano Nunez struck a hat-trick for Cristal as they stormed to a four-goal lead at half-time before Cesar Vallejo scored a second-half consolation goal.
Melgar dropped to third spot on goal difference after a 2-2 draw with Real Garcilaso, while Union Comercio moved into fourth ahead of reigning champions Universitario after a 1-0 win over Juan Aurich.
Universitario conceded an equaliser in second-half stoppage time against Inti Gas to draw 1-1, while Cienciano prevailed 4-2 in a thriller with Leon de Huanuco.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.