Owen, who previously won the Welsh Under-20 crown at the Championship, powered to first place to make it a double.
She beat second-placed Beth Kidger of Brighton by 11 seconds to win the event at Singleton Park in Swansea in a time of 21.31 minutes.
A delighted Owen said: “The course was quite tough but not too muddy. I didn’t expect to win but I wanted to medal.
“I didn’t know who the competition was and didn’t get the lead until around 800m to go.”