Juan Reynoso's men capitalised on the hosts at the Estadio Municipal Francisco Mendoza Pizarro, with Los Caimanes going down to 10 men shortly after the interval.
Ex-Peru international Mario Gomez was sent off in the 48th minute, and Melgar promptly led seven minutes later via Ysrael Zuniga.
Defender Willy Rivas forced a turnover in midfield, charged down the right channel and found striker Bernardo Cuesta who flicked back for Zuniga, the latter thrashing home the opener from outside the penalty area.
The points were sealed when Omar Fernandez's attempted shot was dragged across goal and into the path of Cuesta, who tapped in at the back post in the 85th minute.
Fernandez added a third himself, poking home in the third minute of injury time as Melgar preserved their clean record of zero goals conceded this season.
Leon de Huanuco moved second on seven points, level with Alianza Lima, after a 3-0 win at home to Juan Aurich.
Diego Manicero struck a brace, either side of a John Galliquio goal, to preserve Leon's unbeaten status.
Alianza left it late to see off Universidad San Martin 2-1, Victor Cedron scoring an 83rd-minute winner for the hosts in the capital.
Union Comercio reeled off back-to-back wins to sit fourth on six points, downing UTC Cajamarca 3-0.
Cristian Bogado's penalty on the stroke of half-time put Union ahead, before injury-time sealers from substitutes Jose Ayala and Antonio Meza Cuadra.
