Los Caimanes won the Segunda Division in 2013 to gain promotion to the Primera but had to wait until their ninth game of the campaign to earn their maiden victory, coming from behind to defeat San Simon 4-2.
Roberto Jimenez struck a hat-trick for Los Caimanes, including a pair of penalties, as the Chiclayo-based club leapfrogged Sport Huancayo in the standings.
In the other Sunday match, Inti Gas moved into top spot with a 2-0 victory over reigning champions Universitario.
Inti Gas rose to 18 points, one ahead of Juan Aurich, Cesar Vallejo and Melgar.
At the Estadio 25 de Noviembre, San Simon took the lead in front of their home fans in the 14th minute, when Diego Chavarri thrashed the ball into the net from 20 yards after his initial free-kick bounced back off the defensive wall.
Jimenez equalised for Los Caimanes in the 33rd minute with a spot-kick, while the visitors took the lead in first-half stoppage time when Angel Ojeda thumped a 25-yard drive past Federico Nicosia.
In a frantic finish to the match, Los Caimanes stretched their lead with nine minutes left, with Jimenez tapping in Elsar Rodas' cross, before Miguel Silva dragged a goal back for the hosts three minutes later.
But Los Caimanes secured victory in the 90th minute when Jimenez converted from the spot to complete his hat-trick.
Inti Gas replaced Melgar at the top of the standings with their win on Sunday, scoring twice in three first-half minutes through Jesus Arismendi and Amilton Prado.
Aurich claimed second with a 2-1 victory over Union Comercio, while Cesar Vallejo sit third after a 3-2 triumph over Sporting Cristal.
Melgar drew 1-1 with Real Garcilaso to drop to fourth, while Cienciano moved ahead of Universitario into fifth with a 2-2 draw at Leon de Huanuco.
In other results, Universidad San Martin thrashed UTC Cajamarca, while Alianza Lima prevailed 4-3 in a seven-goal thriller with Sport Huancayo.