Oribe Peralta gave Mexico the lead just six minutes in but the hosts fell apart after the break, succumbing to only their second home loss in 78 World Cup qualifying matches.
Defeat puts El Tri out of the automatic World Cup spots as they sit behind the USA, Costa Rica and Honduras in fourth place, with a trip to Ohio to take on the Americans in prospect on Tuesday.
The top-three finishers will qualify for the World Cup, while the fourth-place team will play a one-game playoff against Oceania champion New Zealand for a spot in Brazil next summer.
Mexico, who have qualified for the last six World Cups, are now winless in seven qualifying matches - losing twice and drawing five - and their hopes of reaching Brazil hang by a thread.
Desperate to keep his job, Mexico coach Jose Manuel de la Torre made a bold move against the Central Americans by benching striker Javier 'Chicharito' Hernandez, who recently returned from a hamstring injury. Peralta got the call up front in the Manchester United star's place, and he was the one shining star for El Tri.
Peralta ended Mexico's scoring drought at home on six minutes thanks to the speed of Giovani Dos Santos, who raced through an unbalanced Honduras defence to find his team-mate on the right to knock in his seventh career international goal.
El Tri looked like a team on a mission throughout the rest of the first half despite not creating any further scoring opportunities before the interval, but Honduras rallied after the break.
Well into the second half, searching for their first scoring chance of the match, Honduras coach Luis Fernando Suarez put Bengston into the action and the momentum swung towards the visitors
In the 64th minute, a long free-kick into the box found Oscar Boniek Garcia, who fired a left-footed shot on goal. Goalkeeper Jesus Corona couldn't control the rebound and Bengston was the man on the spot to knock it in.
It was Honduras' first away goal in the Hex, but it wouldn't be the last. Three minutes later, Costly took advantage of a long clearance and fired a low shot into the far corner.
Mexico struck the post and Costly missed a gilt-edged chance in a frantic finale, but Honduras hung on to close out a famous win.