England international Nobbs netted either side of a red card for County’s Laura Bassett in the first half, while Chioma Ubogagu added a late third to secure Pedro Martinez Losa's first trophy since taking charge of the Gunners in August 2014.
County almost went ahead 10 minutes in at Rotherham's New York Stadium, with goalkeeper Sari van Veenendaal forced into a fine stop to deny Bassett the opener.
However, the Gunners responded when Nobbs raced through on the right to beat Carly Telford after 26 minutes.
County struggled on after being reduced to 10 players, and almost hit back as Jemma Rose and Dominique Janssen had to clear the ball off the line for the Gunners.
But Arsenal were too strong in the end as substitute Ubogagu netted seconds from the final whistle, ensuring that the Gunners have now gone 11 years without a trophyless season.