Monson took the lead over 2018 NCAA runner up Weini Kelati of New Mexico just after the 4,000-meter mark and finished nearly 10 seconds ahead of Kelati.
"It's definitely a difficult course," Monson said. "You've got some hill elements in there so my strength definitely comes in well for that."
Senior Amy Davis improved 10 spots from last year, finishing 15th with a time of 20:14.0. Two other Badgers finished in the top 60: sophomore Lucinda Crouch (43rd, 20:41.5) and senior Alissa Niggemann (59th, 20:41.5).
Top-ranked Arkansas won the team title with 62 points. UW (217 points) was the top Big Ten Conference team.