But Real responded with an equaliser from Benzema after 22 minutes.
The French international surged towards the penalty area and played a neat one-two with Marco Asensio before curling a low finish into the bottom right-hand corner past Guillermo Ochoa.
Real coach Carlo Ancelotti made wholesale changes at half-time, with seven substitutions, which included Benzema making way for Rodrygo and Asensio coming off for Hazard.
Hazard did not take long to make an impact, converting a 55th-minute spot kick after America defender Salvador Reyes was adjudged to have fouled Lucas Vazquez in the box.
Hazard’s penalty looked like settling a drab encounter but America got back on level terms eight minutes from time when Vinicius made the slightest of contact with Fidalgo just inside the area.
Fidalgo, who started his professional career with Real Madrid's B team but did not graduate to the senior squad, stepped up to convert the penalty.
Real Madrid conclude their US tour on Saturday against Juventus at the Rose Bowl in Pasadena, California.