Daniel Ahmed's men broke down Cienciano twice in the quarter-hour following the half-time interval, with each of Luiz da Silva and Edinson Chavez on target in the 2-0 win.
Lima's trip to Union Comercio was postponed, allowing Cristal to go top with 29 points - two clear of Alianza who have a game in hand.
A well-worked move starting with Alexis Cossio in the left attacking corner resulted in the opening goal.
Cossio tracked down a ball on the left byline, played a ball back for Irven Avila, whose one-touch pass released Carlos Lobaton behind the Cienciano defence - and the midfielder's cross to the back post found Da Silva, who nodded across goalkeeper Diego Morales.
Cossio was again involved in the build-up six minutes later as Cristal doubled their lead, as his low cross evaded all comers - but Horacio Calcaterra collected on the right side of the box, and played in Sergio Blanco.
Blanco's shot was saved, and Chavez acted quicker than Cienciano defender Javier Asenjo to tap home in the 59th minute.
Third-placed Melgar joined Lima on 27 points - they have played two more games than the capital club - with a 2-1 home win over San Simon.
They did it the hard way, though, as second-bottom San Simon threatened a boilover when Hilden Salas' 27th-minute goal still had them ahead well into the second half.
But a Minzun Quina penalty restored parity for Melgar, before Bernardo Cuesta's winner.
Cesar Vallejo ended a run of six losses in all competitions, downing Universitario 2-1 away from home.
Fifth-place Universitario missed the chance to usurp Union Comercio in fourth, but stayed ahead of Juan Aurich in sixth after the latter lost 3-1 to Inti Gas.
Inti Gas climbed seventh with their second successive victory, which came courtesy of a second-half brace to Carlos Orejuela.
Victor Rossel was sent off late for Sport Huancayo, as they earned a point at Los Caimanes in a 0-0 draw, while Real Garcilaso's hosting of Universidad San Martin was postponed.
