The New England Revolution striker knocked in the winner, aided by a blunder from a US defensive unit with relatively few FIFA World Cup qualifying caps while American veteran Carlos Bocanegra was watching from the bench.
Juan Carlos Garcia netted a spectacular bicycle kick for Honduras to equalise in the 39th minute after the visitors had seized the lead following a goal by Tottenham's Clint Dempsey in the 36th minute.
The critical stretch began when Oscar Garcia pushed the ball past US defender Geoff Cameron. US goalkeeper Tim Howard came after the ball but Garcia flicked the ball past him into the empty penalty area where an onrushing Bengtson kicked it home before a sliding Omar Gonzalez could stop him.
Maynor Figueroa took a centering pass on the chest and deflected the ball into the crowded heart of the penalty area, where Garcia made an incredible somersault and followed with a hammering kick past Howard.
Dempsey put the Americans ahead 1-0 by taking a perfect lob pass from Jermaine Jones in full stride while leaping into the air on a run midway through the penalty area.
Without an instant's pause, Dempsey blasted the ball past Honduran goalkeeper Noel Valladares to open the scoring.
Honduras boss Luis Fernando Suarez told reporters: "The win is quite nice but this is only the first step.
"The team did interesting things on the field and always went towards the rivals' goal. This is a totally deserved win and it is because the team played better."
"The final score shocked us, even though we know playing Honduras home or away is very hard. Now we must win the next games because we must get into the World Cup."