Man of the Match Suarez grabbed his double in nine first-half minutes, the second an audacious 40th minute chipped penalty, before Gaston Pereiro completed the scoring on the hour mark with his first international goal.
Jimenez could have pulled one back for Mexico, but his second penalty of the match was saved by keeper Fernando Muslera with 16 minutes remaining.
In Los Angeles, a new-look Argentina, missing Lionel Messi, who is taking a sabbatical from international football, and the retired Javier Mascherano, were still too strong for an inexperienced Central American opposition.
Gonzalo Martinez got Argentina's first from the penalty spot after 27 minutes, before Giovani Lo Celso doubled their lead eight minutes later with a sweetly struck half volley from 25 meters.
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Giovani Simeone, son of Athletico Madrid manager Diego Simeone, scored the third on his national team debut two minutes before halftime to complete the scoring.
The game petered out in a second half following a raft of substitutions but the win was a welcome tonic for a team that disappointed in Russia, handing caretaker coach Lionel Scaloni a solid start.
"Ever since I was a boy my dad told me that one day I would be here," a delighted Simeone told reporters. "No matter the rival, there was a lot of anxiety to see this new Argentina. In the first half we did everything we had to do."
In another friendly involving South American sides in the United States, Colombia came from behind to beat neighbours Venezuela 2-1 in Miami.
Darwin Machis put Venezuela ahead after just three minutes, but Radamel Falcao equalised with a header nine minutes into the second half before Yimmi Chara got the final touch to a goalmouth scramble to seal Colombia's win in the last minute.
Argentina take on Colombia in New Jersey next Tuesday, the same day Mexico play the United States in Nashville.
Guatemala play Ecuador in Bridgeview, Illinois, while Brazil, who beat the U.S. 2-0 earlier on Friday, go to Maryland to play El Salvador.
(Reporting by Andrew Downie; Editing by John O'Brien)
