Brandon Vincent turned Julian Gressel’s cross into his own net before Johan Kappelhof was sent off for bringing down Martínez, who would have been through on goal.
The forward doubled the hosts’ advantage on the hour mark and Héctor Villalba lashed home inside the area just seven minutes later.
Martínez scored his second of the game with a clever finish from a tight angle to send Atlanta to their second victory in succession in their debut MLS season.
Atlanta go ahead early before Chicago sending off
Gressel collected Villalba’s pass and drove a low cross across the area, a cross that was diverted into his own net by Vincent.
It wasn’t long before the next incident occurred, Martínez looked to be through on goal, only for Kappelhof, who was the last man, to bring him down and the defender received his marching orders.
Martínez was denied by a brilliant last-ditch block by Vincent on the edge of the area, and Jorge Bava managed to scramble to his near post to push Yamil Asad’s shot behind.
Chicago’s first opening came on the stroke of half-time when substitute Jonathan Campbell headed João Meira’s into the arms of Atlanta’s ‘keeper.
Martínez and Villalba press home advantage
United doubled their advantage in the game on the hour mark when Miguel Almirón threaded a pass through to Martínez.
The Venezuelan international showed great composure to take the ball in his stride and go round the ‘keeper before tapping into an empty net.
Atlanta pressed home their man advantage and found another opening in the game seven minutes later after a swift break forward.
Greg Garza’s cross could only be cleared out as far as Villalba, who latched onto the ball and smashed his shot into the top corner.
Chicago could have brought themselves back into the game just minutes later when David Accam forced Alec Kann into a good reaction save.
The midfielder handed the ball off to Arturo Álvarez out wide before darting into the penalty area, he met the cross at the near post and was denied by a great stop.
Martínez nets second in final eight minutes
Atlanta inflicted more misery on their opponents eight minutes from time when Martínez showed his class once more.
Asad picked out the forward, who took the ball round the ‘keeper for the second time in the game before slotting home from an incredibly tight angle.
The hosts were still gunning for more goals and the visitors’ heads had dropped, Leandro González Pirez nodded Asad’s cross down into the ground, but the ball then bounced over the bar.