Pumas, in their second match under Jose Luis Trejo, went down 1-0 at home in Mexico City to new leaders Morelia and remain one place off the bottom of the standings.
Morelia benefited from champions America's 2-1 defeat, their first of the season, at Santos Laguna on Friday.
Morelia have 20 points from 10 matches, one point more than America, who have two games in hand, and Leon.
Striker Hector Mancilla scored the only goal at the Olimpico to leave seven-time champions Pumas with five points from 10 matches.
Coach Trejo said the players sometimes lacked confidence and they had to find a way to overcome that.
"We faced one of the best teams (in the league) but I didn't view the match as one we should have lost," he told reporters. "At home these things can't happen to us."
A late equaliser from Chivas forward Marco Fabian salvaged a 2-2 draw at home to Tijuana but they remain four from bottom with seven points and just one win in nine matches.
Chivas have managed three draws under coach Juan Carlos Ortega, who replaced the sacked Benjamin Galindo towards the end of last month.
Guadalajara owner Jorge Vergara, whose experiment with Dutch great Johan Cruyff's consultancy last year ended in failure, admitted earlier this month to making mistakes since he bought the club in 2002.
"I made mistakes more than once, I confused arrogance with knowledge and sense (but) it's never too late to correct and change attitude," Vergara told reporters.
In 13 years under Vergara, Chivas, who hold a record 11 league titles jointly with America, have won only the 2006 Apertura and had 17 different coaches.
Failure is first measured in the Mexican first division by not making it to the knockout phase of the championship when the top eight teams in the 17-match league phase play for the title.
Guadalajara are currently seven points behind eighth-placed Toluca, while Pumas are nine points adrift.