Tangela Smith scored 25 points and pulled 74, in Game 1 of the Eastern Conference Finals.
Tamika Catchings, who was named the MVP of the WNBA on Thursday, had 12 points and 13 rebounds while Katie Douglas and Shavonte Zellous each added 11 points for the Fever, who defeated New York in three games in the semifinals.
Lindsey Harding had 17 points and seven assists while Sancho Lyttle added 14 points and seven boards for the Dream, who swept the Sun in their semifinal series.
Game 2 of this best-of-three series is set for Sunday in Atlanta.
The Dream took a three-point lead into the second quarter, but saw that lead evaporate early on consecutive three-pointers from Smith and Zellous.
That helped the Fever take a 42-40 lead into the break and the game stayed close in the third with Harding putting in a layup late to tie the game at 57 heading to the fourth.
Holding a one-point lead, the Fever got a bucket from Zellous and Smith followed with a three-pointer for a 68-62 advantage.
Tammy Sutton-Brown then dropped in a layup for an eight-point lead with 4:15 to play.
The Dream were able to get as close as five, but the Fever hit their free throws down the stretch to hold on.