Kara Lawson added 16 points for the Monarchs, who can capture their first-ever WNBA championship with a win Tuesday night.
Nykesha Sales had 17 points to lead Connecticut, while Taj McWilliams-Franklin had 16 points and 13 rebounds in the loss.
The Sun need to win Game 4 to avoid losing in the Finals for the second-straight year. They lost in three games to the Seattle Storm in 2004.
Connecticut guard Lindsay Whalen started and scored just two points in 23 minutes. Whalen, the third-leading scorer for the Sun in the regular season, missed Game 2 with a left knee injury.