Fentanes' predecessor Jose Luis Sanchez quit after Ricardo Henaine bought rival Francisco Bernat's 51 percent share to take a 94.6 percent stake in the club.
"I love this club and my players deeply but the hatred I feel for Ricardo Henaine is greater, that's why I'm stepping down," Sanchez told reporters when he quit.
Fentanes, who was former Mexico coach Ricardo La Volpe's assistant at the 2006 World Cup in Germany, had been Sanchez's right hand man since 2007.
Puebla are second in Group Three, four points behind Cruz Azul, who beat Tigres UANL 3-2.
Javier Orozco scored his fifth goal in two matches for Cruz Azul having netted four in the 5-4 home win over Real Salt Lake of the U.S. in a CONCACAF Champions League game on Wednesday.
Jose Luis Mata, another former assistant promoted to head coach, had a losing debut with Atlas on Saturday.
Atlas, who sacked Argentine Carlos Ischia last weekend, are rooted to the bottom of Group Two with one point after a 3-1 defeat away to Group One leaders Santos Laguna.
Title holders Toluca beat Queretaro 2-0 and are top of Group Two on goal difference from America, held 1-1 by Necaxa at the Azteca.
The championship is divided into three groups but the teams all play each other once. The top two in each group after 17 matches plus the next two best placed teams qualify for the quarter-finals.
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