Several hundred fans gathered in the twilight on Court 10 of the Billie Jean King National Tennis Center to watch the match, which was among those delayed several hours by rain.
Among them were Cohen's father, Richie, a longtime Philadelphia-area club player. Cohen's mother, Nancy; her brother, Josh, the coach of the Philadelphia Freedoms; and former tour pro Murphy Jensen were also on hand.
Displaying powerful ground strokes that were simply too much for Cohen, Rodionova, the No. 163 player in the world, broke No. 101 Cohen twice in the first set, taking it with a forehand volley winner.
The second set lasted just 27 minutes, and the match ended when Cohen sailed a two-handed backhand long.
"She played well today and I didn't play my best match," said Cohen, who picked up $23,000 for her efforts, or about 10 percent of her career earnings thus far.
After failing to qualify for the U.S. Open in several previous years, Cohen finally qualified after cracking the top 100 in the world by reaching the final of an event in Baku, Azerbaijan, in late July.