With Santos Laguna held to a 2-2 draw at Monterrey on Saturday, Pumas took advantage to move into third, seven points adrift of second-placed Toluca, who had lost 3-1 to Tijuana on Friday.
Dante Lopez scored twice in the first half for Pumas and although Aviles Hurtado hit back for Chiapas in the 79th minute with a bicycle kick, the home side held on for victory.
The win took Pumas to 21 points after 14 rounds in the Mexican Clausura campaign, just ahead of Santos Laguna on goal difference, while Toluca's second loss in three matches left them on 28, four points adrift of leaders Cruz Azul.
Toluca midfielder Jorge Luis Sartiaguin cancelled out Dario Benedetto's opener for the home side before half-time but Tijuana ran away with the game in the second half thanks to goals from Javier Guemez and Cristian Pellerano, the latter from the spot.
At the Estadio Olimpico de Universitario, Pumas opened the scoring in the 35th minute when Lopez put the pressure on Chiapas goalkeeper Alfredo Frausto, won the ball and converted from close range.
Lopez's second goal came in first-half stoppage time as he tapped in at the back post after fine lead-up work from left-back Efrain Velarde.
Chiapas gave themselves a lifeline with 11 minutes remaining when Hurtado's bicycle kick from a corner found the back of the net.
But the visitors were unable to trouble the scorers again as they failed to avoid their fifth defeat in eight games in all competitions.
In the other match on Sunday, Tigres UANL won 2-0 at Atlante.
On Saturday, Cruz Azul ended their winless streak at two games, as they trumped America 2-1.
Mauro Formica's 18th-minute header from a corner put Cruz Azul ahead at America's Estadio Azteca and the visitors doubled their lead two minutes before the break when Julio Dominguez flicked on Rogelio Chavez's free-kick with his head.
America were reduced to 10 men in the 74th minute when substitute Andres Andrade received his second yellow card in four minutes but the home side ensured a nervous finish for the Liga MX leaders when Raul Jimenez scored with a fine volley in the 86th minute.
Cruz Azul held on, however, and America finished the match two players short after Rubens Sambueza received his marching orders in the third minute of stoppage time.
Santos Laguna had to come from two goals down to earn a draw at Monterrey with Sergio Ceballos scoring on the hour mark and Oribe Peralta notching the equaliser in the 89th minute.
The draw left Santos Laguna just ahead of America, Pachuca, Tijuana and Guadalajara, who are all on 20 points.
In other results, Guadalajara won 3-1 at Pachuca, Morelia drew 1-1 with Veracruz, Atlas versus Puebla finished goalless and Leon were held to a 1-1 draw by Queretaro.
