Antonio Mohamed's America had won all five of their games in Apertura prior to Saturday's fixture, accounting for defending champions Leon, Tijuana, Puebla, Tigres UANL and Morelia.
But America's blistering start to the season came to a halt, dropping points after playing out a goalless draw at Chiapas.
Chiapas and America had chances to claim maximum points at the Estadio Victor Manuel Reyna Stadium but the two teams were forced to share the spoils.
America's stalemate saw the club move to 16 points from six games, three clear of rivals Monterrey, who edged Puebla 1-0.
Liga MX's leading goalscorer Dorlan Pabon proved the difference in the 67th minute after rounding goalkeeper Rodolfo Cota, albeit with some help from a deflection, and tapping the ball into an empty net.
Pabon - recruited from Brazilian outfit Sao Paulo on loan - has scored seven goals, with five of those coming in his past three matches.
Back-to-back wins has Monterrey (+5) level on 13 points with Atlas (+4), who were beaten over the weekend.
Atlas had no answer as Matias Alustiza's hat-trick inspired Pachuca to a comprehensive 3-1 victory on Saturday.
Alustiza headed across goal to open the scoring on the stroke of half-time and he was at it again four minutes into the second half.
The 30-year-old weaved his way past three Atlas defenders before side-stepping keeper Federico Baudena for his second of the match.
Alustiza completed his three-goal haul with a 74th-minute penalty, while Atlas netted a consolation through Arturo Gonzalez four minutes later.
In other results, a four-goal second half helped Tigres UANL to a 5-1 rout of basement-club Morelia on Friday.
Guido Pizarro, Emauel Villa, Hernan Burbano and substitute Damian Alvarez were all on target as visiting Tigres ran rampant at the Estadio Morelos to climb up to sixth in the standings.
Morelia dropped to the foot of the table after Universidad Guadalajara stunned Leon 1-0 on Sunday.
In Friday's other match, Santos Laguna moved fourth in the table with a 3-0 victory at home to Toluca.
On Saturday, Cruz Azul accounted for Queretaro 2-1 and Guadalajara held Veracruz to a goalless draw.
Meanwhile, Pumas UNAM and Tijuana share the spoils after a 1-1 draw on Sunday.
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