Two minutes later, Mata struck the base of the post with a 20-yard shot which had Club America goalkeeper Agustin Marchesin beaten.
Martial, who has been linked with a move away from Old Trafford this summer, was lively in the first half and it took two deflections to divert his 23rd-minute strike wide after a driving run forward.
One man who has joined Martial at United is Lee Grant, and the 35-year-old goalkeeper made a couple of important saves to keep the Red Devils level at the interval.
The former Stoke City stopper got a strong left hand down to deny defender Paul Aguilar and then blocked a powerful hit from Club America striker Roger Martinez, who had bulldozed through the United defence.
Both managers made wholesale changes in the second period, with Joel Pereira replacing Grant in goal and the 21-year-old was quickly into action as he raced off his line to stand up tall and thwart Martinez in a one-on-one.
However, there was nothing that Pereira could do to keep out Martin's 59th-minute header which nestled into the top corner.
The amount of substitutions - 17 in total - took the sting out of the game somewhat but United's 18-year-old winger Tahith Chong brought some impetus off the bench and played a crucial role in Mata's equaliser.
The Dutchman checked back onto his left foot to whip in a deep cross which Herrera headed against the post. A miscued clearance fell to Mata who squeezed a shot through two defenders and replacement goalkeeper Oscar Jimenez.
Mourinho had lost Martial to a knock which harmed United's chances of pushing for a winner, so the Red Devils boss was content to give minutes to teenagers Angel Gomes and Mason Greenwood, making his debut at only 16 years old.
United are back in action on Sunday when they face MLS opposition in the form of San Jose Earthquakes.
CLUB AMERICA (4-5-1): Marchesian (Jiminez, 72'); Aguilar, Alvarez (Zamorano, 65'), Aguilera (Leon, 45'), Reyes (Torres, 58') ; Ibarguen (Moreno, 45'), Ibarra (Lopez, 45'), Martin (Garcia, 67'), Corona (Rangel, 45'), Rodriguez (Arce, 45'); Martinez (Gonzalez, 58')
MAN UTD (4-3-3): Grant (J.Pereria, 46'); Valencia (Fosu-Mensah, 46'), Bailly, Smalling, Shaw (Greenwood, 76'); Herrera, McTominay (Tuanzebe, 87'), A. Pereria; Mitchell (Chong, 60'), Mata (Gomes, 87'), Martial (Darmian, 60')