The crowd of 18,626 at the Home Depot Center in California was largely pro-Honduras, and they were delighted by Palacios's header off a cross from Pavon, as well as Espinoza's crisp strike.
The hosts were a man down for much of the match, after defender Jimmy Conrad was ejected by Mexican referee Benito Archundia in the 17th minute for his second yellow card.
"It's tough to fight back, especially a man down," said Jonathan Bornstein, the closest to a regular in the US lineup. "The match just didn't go our way this time."
For the USA, the match was the conclusion of a 19-day training camp that featured a largely US-based talent pool trying to play their way on to the South Africa 2010 squad. Ten players from a similar camp in 2006 made the final FIFA World Cup squad for the US.
The Americans, preparing for a sixth consecutive FIFA World Cup appearance, will face England on 12 June in their opener in South Africa and also face Slovenia and Algeria in first-round matches. Honduras, which qualified for the first time since 1982, will open 16 June against Chile and shall also face Spain and Switzerland.