The Black Stars struck in the second half but it was Blessing's Kansas City side who ran out 3-2 victors at Children's Mercy Park.
Daniel Salloi was the first to get on the scoresheet.
The Hungarian latched onto a loose ball in his own half, took a solo run, before firing a shot into the roof of the net to give KC the opener on 23 minutes.
But Fire were soon back in the game after five minutes as Matt Besler scored into his own net to restore parity.
Benny Feilhaber then put KC back in front with an overhead kick of a rebound on the stroke of half-time after goalkeeper Matt Lampson parried out Blessing's header.
Six minutes after recess, it was Blessing's turn to get on the scoresheet.
Having found space in the goal area, the former Liberty Professionals man had the easiest jobs of putting a slight deflective touch on Diego Rubio's shot to take KC 3-1 up.
The goal was the 20-year-old's third in 14 MLS appearances this season.
But it was not all over at Children's Mercy Park as Accam tapped in from close range to reduce the deficit for Fire.
The Right to Dream graduate's strike 12 minutes to full-time took his season tally to 12 goals in 19 matches, leaving him as the Men in Red's current highest scorer of the campaign.