America, who finished the game with nine men after two players were sent off in the final 12 minutes, saw their lone goal come on a penalty kick by Alfredo Moreno in the 33rd minute.
Oduro put the home side up 1-0 in the ninth minute thanks to a great assist from Bruno Guarda. The Brazilian midfielder dribbled almost to the touchline, taking an America defender with him, then laid the ball off to Oduro, who was about seven yards from goal. The Ghanaian striker then calmly sent it into the far side of the net.
Cooper too benefited from a great assist, his coming from fellow Dallas native Drew Moor in doubling the lead. The FCD captain dashed up the right flank and spotted his teammate open in virtually in the same spot from where Oduro scored minutes prior. Moor hit a perfect ball and Cooper then finished with a shot into the far side of the net to make it 2-0.
In the 33rd, America drew a goal back after Moreno converted a penalty kick. He stepped to the spot after Moor took him down about 10 yards from goal. FCD goalkeeper Dario Sala went the right direction, going right, but Moreno hit his shot inches over Sala's outstretched hands.
America's Alejandro Arguello was ejected in the 78th minute after delivering a hard elbow to the head of Guarda, then the Aguilas dropped to nine men in the 89th minute when Antonio Castro was sent off for a hard kick to FCD forward Jamie Watson near the far sideline.
FCD head coach Schellas Hyndman used a lineup sprinkled with starters and reserves. Up top, he went with Cooper and Oduro. The Hoops' midfield consisted of Dax McCarty on the right, Guarda and Pablo Ricchetti in the middle with Eric Avila on the right.
In the back, Hyndman went with Blake Wagner on the left, Brek Shea and Aaron Pitchkolan in the middle with Drew Moor wearing the captain's armband on the right flank. Dario Sala started between the posts.
Early on, the FCD attack was on the offense. In the second minute, a slow roller by Cooper toward the America goal was saved by 'keeper Armando Navarette. Three minutes later, Oduro got his first serious look at goal when he blasted an attempt toward the far post but Navarette delivered a great diving save to deny him.
But following the America goal, the Aguilas attack came to life as Rafael Marquez had a pair of chances at the equalizer in the 35th minute. His first opportunity came when he shot the ball high. But literally seconds later, Marquez was unmarked at the far post, but put his uncontested header high over the goal.
In the 43rd, Marquez was active yet again and this time nearly converted, but his shot plastered the right post at the last moment. Seconds later, the America striker struck a great ball from 20 yards out but Sala made a diving save to deny his effort.
At the break, America held the edge in shots 11-7 with six of the Aguilas' efforts being denied by Sala.
America continued their push in the second half when in the 48th minute, Juan Carlos Mosqueda hit one right at Sala.
In the 54th minute, things got a little interesting when Oduro and Navarette collided on a 50-50 ball about 13 yards from goal and both fell to the ground hard. With the net open, McCarty had a chance at making the game 3-1 but his shot was offline.
As the half progressed, America got stronger. Marquez fed Moreno in the 59th about 20 yards from goal but Sala was once again there to deny.
The chances for FCD were few and far between in the second half but in the 62nd, the Hoops were awarded a free kick about 30 yards out. Cooper stepped up and took it but his effort was more of a slow roller that was well-played by Navarette.
In the 65th minute, Hyndman went to his bench bringing on Andre Rocha for Avila and taking out McCarty for Jamie Watson.
After a shot by Watson was saved by Navarette in the 71st, things got heated when Arguello was sent off. The America striker delivered an apparent high elbow to Guarda that drew blood and was quickly ejected by referee Jason Anno.
In the 89th, things again got heated when Castro kicked Watson hard on the far sideline. Matters got tense enough that security personnel dashed over to defuse the situation.
Sala finished the night with nine saves and was clearly the star of the afternoon for FCD. The Hoops, who are 0-3-1 in their last four league games, return to MLS action next Saturday when they face D.C. United at RFK Stadium.