Bengtson, who had both goals in Thursday's opening 2-2 draw with Morocco, scored again off a cross from Roger Espinoza to eliminate Spain with its second loss at the Games and put Honduras on the verge of the quarterfinals.
CONCACAF's other hopeful, Mexico, also edged closer to the knockout round, getting a second-half pair of goals from Giovani Dos Santos - the finale a penalty in injury time -- to beat Gabon 2-0.
The result gave Mexico four points atop Group B, equal with Switzerland and three better than Gabon and South Korea with the group leaders set to play Wednesday.
In Newcastle, England, after taking the lead, Honduras spent much of the rest of the match in its own end. Spain repeatedly sent shots just side, hit the post or crossbar three times while Honduran keeper Jose Mendoza made a handful dramatic saves to preserve the victory.
"Los Catrachos" climbed to second place in Group D with four points, two behind Japan and three better than both Spain and Morocco. Honduras will need only a draw in its group finale against Japan on Wednesday to assure passage into the quarterfinals.
Espinoza and Andy Najar traded passes on the left side before Espinoza sent a cross into the middle of the area, where Bengtson outdueled Jordi Alba and drove a header inside the left post while Spanish goalkeeper David De Gea didn't even take a step.
But Spain repeatedly threatened after that, with Juan Matta missing by less than a meter three times in the first half, Adrian Lopez, Iker Muniain and Rodrigo Moreno all putting shots off the frame in the second half, and Mendoza diving to his right to deny Rodrigo in the 71st.
Spain intensified its efforts as time dwindled, but Honduras prevailed for its first victory at the Games since defeating host Australia in the first round in 2000.
In Coventry, England, Mexico was frustrated on its handful of chances for the first hour by Gabon keeper Didier Ovono Ebang.
Mexico created several opportunities in the first seven minutes with Hector Herrera and Marco Fabian testing Ebang, and Miguel Ponce volleying a cross wide at the left post.
Oribe Peralta also had chances, but Dos Santos, who entered in the second half in the opening 0-0 draw with South Korea, replaced Ponce in injury time of the first half against Gabon.
Peralta and Javier Aquino both had shots denied by Ebang before Peralta settled a long ball at the top of the area, squared it left to Dos Santos who touched it further left to create more space. With an alley to shoot, he skipped a shot low inside the left post past Ebang in the 63rd minute.
Dos Santos added the penalty in the second minute of injury time after Peralta was shoved from behind by Gabon defender Henri Ndong, a foul which also resulted in his ejection.