The Western Conference Player of the Week knocked down 8-of-14 from the floor, including 4-of-7 from the three-point line to lead the Lynx to the victory.
Augustus scored 21 points and five assists on 7-of-15 shooting and Rebekkah Brunson added 12 points.
Connecticut was in front early, but the Lynx bounced back in the second quarter to take a 42-40 lead into the break. Minnesota stretched that lead in the third, holding the Sun to just 14 points in the quarter.
But the Sun had enough energy for one more run. During a 9-0 stretch of the fourth quarter Connecticut regained the lead, 63-62.
Alex Bentley led the Sun with 22 points. She knocked down 4-of-8 from behind the three-point line. Kelsey Bone and Camille Little each added 13.
The Lynx fought back down the stretch, though, making all five of their free-throws in the final minute to put the game away.