The Argentine midfielder was sent off after half an hour at the Azteca for retaliating to a tackle but the Eagles clung to the eighth minute lead they took with a goal by Mexico defender Miguel Layun.
America are in second place one point behind Cruz Azul, the only unbeaten team in the Clausura championship after five matches with 13 points following their 2-0 victory away to Guadalajara at the Omnilife.
Toluca lost ground after a 2-0 defeat at Santos Laguna to drop three points off the pace.
America coach Antonio Mohamed had said on Friday that fines had helped his compatriot Sambueza curb his aggressive nature and become more valuable for his team.
"I'm not going to talk about that (red card) situation because the foul was on him, whether he was provoked or not, or whether it was (only) a yellow (card offence)," Mohamed told reporters after the match.
"The dismissal complicated things a lot for us... (but) in the end it's a win, we value the players' commitment," Mohamed said.
"The team overcame adversity, we felt the fatigue of the players who travelled midweek," he added referring to half a dozen America players in the Mexico team who played a World Cup warm-up friendly against South Korea, a 4-0 win, across the Texas border in San Antonio on Wednesday.
Mohamed's predecessor at America is Mexico coach Miguel Herrera who has been building his squad for the World Cup finals in Brazil around players from his former club, including America's scorer Layun.