Costly's header in the 77th minute and Bengtson's 80th-minute blast - off the rebound from his own saved penalty attempt - cancelled out a pair of goals from Javier Hernandez.
The draw left Honduras atop the six-nation final qualifying group in North and Central America and the Caribbean (CONCACAF) with four points.
Regional powerhouse Mexico, meanwhile, remain in search of a first win after two matches, having been held to a goalless draw when hosting Jamaica last month.
Honduras had opened their final-round campaign with a 2-1 victory over USA last month.
The USA were trying to bounce back from that defeat on Friday when they hosted Costa Rica in Denver later on Friday in a match coach Jurgen Klinsmann called a "must-win". In the day's final match, Jamaica host Panama.
The top three teams advance to the Brazil 2014, while the fourth place team plays off against top Oceania team New Zealand for a final berth.
He opened the scoring in the 28th, heading in a cross from the hard-working Andres Guardado on the left.
He doubled Mexico's lead in the 54th, eluding the defenders in front of the goal to slot home a set-piece delivery from Carlos Salcido.
Honduras had few true scoring chances before Costly rose to head in a corner kick in the 77th.
Minutes later, Costly drew a foul in the penalty area and Bengtson stepped up to take the kick.
Guillermo Ochoa dived to his right for the save, but pushed the ball straight back to Bengtson who belted the equaliser past the helpless keeper.