Kara Lawson scored 22 points and made all eight of her free throw attempts to help the Sun defeat the Fever, 88-85, in overtime.
After the Sun went scoreless in the last 2 1/2 minutes of regulation, allowing Indiana to rally from a five-point deficit, the Fever went ahead by two on a Katie Douglas jumper with 2:36 remaining in the extra period.
But just as Connecticut did a period earlier, Indiana went scoreless the rest of the way. Tina Charles scored three of her 14 points on a free throw and subsequent layup with 41.7 seconds left to put the Sun ahead for good.
After Ashja Jones blocked Indiana's Tamika Catchings, Lawson drained the clock to 5.2 seconds and made a jump shot to put the Sun ahead by three. Briann January, who went 2-for-8 from beyond the arc, missed a potential game-tying three in the final moments.
Charles added 14 points and eight rebounds for Connecticut, which moved to 9-2 this season, best in the East. Renee Montgomery and Kalana Greene had 12 points apiece in the win.
Douglas led Indiana with 23 points and nine rebounds, but the Fever dropped to 5-4. Catchings added 14 points in defeat.