Mexico started its World Cup preparations with a 0-0 draw against Wales at the Rose Bowl on Monday night.
Hennessey made several impressive saves, including sticking out his right foot to deny Mexico captain Hector Herrera's shot in the 56th minute from the edge of the 6-yard box.
Hennessey also tipped Herrera's shot from outside the penalty box over the crossbar in the 40th minute and parried away Javier Aquino's attempt in the 22nd minute.
Mexico dominated possession and kept the pressure on a Welsh side mostly lacking in experience at the international level. Their defense settled in well after some early jitters without Nestor Araujo, who left the team Wednesday following a setback in his recovery from a knee injury.
With Mexico always a strong draw in Los Angeles, the international friendly attracted a crowd of 82,345, the largest to see a soccer match in the United States this year.
Mexico's roster also featured three players from the city's two MLS clubs, with brothers Giovani and Jonathan dos Santos representing the Galaxy, and Carlos Vela from expansion team Los Angeles FC, though Vela did not play.
Jonathan dos Santos came on in the 61st minute, and Giovani dos Santos was a 69th-minute substitute.
They finished out the game without any apparent limitations from hamstring injuries that have limited both brothers this season. Mexico manager Juan Carlos Osorio set a Saturday deadline, which coincides with a friendly against Scotland in Mexico City, to prove their fitness and make the final roster.
Wales captain Ashley Williams was subbed out immediately after sustaining an apparent left leg injury when he collided with Mexico striker Javier "Chicharito" Hernandez in the 17th minute.
The Everton defender was replaced by Tom Lockyer of Bristol Rovers. Wales did not have Real Madrid forward Gareth Bale available because of the Champions League final on Saturday. Bale scored twice in the 3-1 win over Liverpool in Kiev, Ukraine, to help Madrid to its third consecutive title in the competition.
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