Angel McCoughtry scored 26 points and 67 win over Indiana in the decisive Game 3 of the Eastern Conference finals.
Iziane Castro Marques added 23 points and Lindsey Harding 16 for Atlanta, which will make a return trip to the WNBA Finals after being swept by Seattle in 2010.
Sancho Lyttle netted 10 points, pulled down 11 boards and had five steals for the Dream, who overcame big odds to make it to the championship series against the Lynx. The best-of-five series starts Sunday at Minnesota.
Katie Douglas had 16 points and nine rebounds for the Fever, while Tammy Sutton-Brown recorded 11 points and nine boards.
Tamika Catchings, this year's league MVP, didn't start Tuesday due to a right foot injury she suffered in Game 2 Sunday. She entered the game with 6:01 left in the first quarter to a standing ovation, but didn't make a big impact as she ended with six points.
Indiana, which lost in five games to Phoenix in the league's title series in 2009. was behind by as many as 24 points and suffered its first-ever loss in a Game 3 at home. It was the first time the Fever lost a playoff series when having home-court advantage.
The Dream swept the Fever in the regular season series, winning all four matchups, but the real story was how Atlanta even got to this point. Atlanta started the season 3-9 but then went on to set a franchise record with 20 wins.
The magic continued Tuesday night, as Atlanta used a 12-2 run in the opening quarter to grab a 23-17 lead following a Harding jumper.
Atlanta was up five after the opening quarter and 39-35 at the half before a three-ball from Castro Marques widened the gap to 46-35. She made all three of her shots from long range in the third, helping the Dream to a 61-47 cushion going to the fourth.
The largest lead of the night came with nearly three minutes left when McCoughtry sank a short jumper for an 80-56 difference.
Minnesota won both of its meetings against the Dream this season, in back-to- back matchups in June by a total of 24 points.