Mexico international Peralta fired the ball beyond onrushing Morelia goalkeeper Felipe Rodriguez in the second minute of added time to preserve America's perfect start to the Apertura season at the Estadio Azteca.
An unmarked Pablo Aguilar opened the scoring for America in the 38th minute with a close-range header.
Duvier Riascos levelled proceedings seven minutes into the second half courtesy of a header that hit the post and came off Moises Munoz's leg in goal.
Scores were level for just five minutes after America's Rubens Sambueza drove into space and unleashed a powerful shot from outside the penalty area.
However, Peralta's 93rd-minute goal - his third in as many games - earned America maximum points against their lowly opponents, who sit second-bottom.
America's run of five consecutive wins has them two points clear of Atlas atop the table.
Atlas were 1-0 victors over cellar-dwellers Universidad Guadalajara thanks to Luis Cabellero's 90th-minute penalty on Saturday.
New recruit and the league's top goalscorer Dorlan Pabon netted a hat-trick as third-placed Monterrey returned to the winners list, toppling Cruz Azul 3-1 on Saturday.
Tijuana ended a run of back-to-back draws after they edged Chiapas 2-1 courtesy of Dario Benedetto's double.
