''Really it was more about effort,'' Phoenix coach Sandy Brondello said. ''We had to play harder. I didn't think we were playing hard as we could and we changed that in the second half.''
Erlana Larkins' short jumper gave Indiana a 52-39 lead midway through the third before the Mercury (10-3) rallied.
Phoenix trailed 61-55 entering the fourth quarter, but Taurasi scored eight points in the final period to finish with at least 20 for the seventh time this season.
The Mercury trailed by 13-points midway through the third quarter, The Mercury finally erased the deficit with a 13-4 run to open the fourth and took a 68-65 lead with 4:32 to play.
With the score tied at 70, DeWanna Bonner stole the ball from Indiana's Marissa Coleman, who was then whistled for a clear-path foul to give Phoenix two foul shots and possession of the ball. Bonner made both free throws and Dupree added a basket to put the Mercury up 74-70 with 2:14 remaining.
''It was a tough game, it just always is when you play Indiana,'' Taurasi said. ''The game is usually really ugly and today was no different. We found a way to play a little bit better towards the end. That kind of was the difference.''
Taurasi earned a flagrant-one foul during the third quarter when she caught Briann January with her right forearm. Then less than a minute later she was issued a technical foul.
Shavonte Zellous led Indiana (6-8) with 18-points, including three free throws with 42.6 seconds left to pull within one.
Phoenix closed out the game with a 3-pointer by Taurasi and four free throws by Bonner.
The Mercury's Brittney Griner was held to a season-low four points - all in the first half.
''Anytime you hold Griner to four points, you're doing really good,'' Indiana coach Lin Dunn said. ''Unfortunately, Taurasi and Taylor gave us some fits, and with some help from Dupree.''
The win marked Phoenix's largest comeback win of the season. The previous mark was 12-points against San Antonio on May 23.