Angel McCoughtry and Jasmine Thomas added 11 points each and rookie Shoni Schimmel had 10 for first-place Atlanta (14-5).
"That is the good thing about this team," Dream assistant coach Karleen Thompson said. "You have to pick your poison. Tiffany has been standing up for us for a while. I think she is the best driver-finisher going to the basket in the league."
Tamika Catchings scored 12 of her 14 points in the third quarter for Indiana (10-11).
The Dream trailed 19-16 before Schimmel's layup with 3:07 to go in the first quarter started a 25-5 run that put them ahead for good. Thomas' 3 with 5:34 to go in the second put Atlanta ahead 41-24, and the Dream led 55-34 at the break.
"We started getting down on defense, we were getting steals and boxing out," Hayes said of the second quarter. "That enabled us to get our transition game going. That is when we are lethal."
The 55 first-half points tied the most an opponent has scored against the Indiana since Minnesota scored 60 on June 7, 2009.
"We didn't defend at a high level and I think in the second half we picked up our defense a little better," Indiana's Shavonte Zellous said.
The Fever cut the 21-point halftime deficit to 66-56 on Karima Christmas' free throw with 2:07 left in the third quarter.
However, DeLisha Milton-Jones made two free throws in the final minute of the period, and Schimmel made a 3 with to open the fourth and push the Dream's lead to 73-58.
The Fever got no closer than 11 the rest of the way.
Briann January added 13 points for Indiana, but left the game with 3:08 to play in the third quarter with right knee pain after colliding with Schimmel. Erlana Larkins record her sixth double-double of the season Indiana with 10 points and 11 boards.