Larkins finished two rebounds shy of the WNBA single-game record set by Washington's Chamique Holdsclaw at Charlotte on May 23, 2003.
The Fever (1-3) ended a three-game losing streak that stopped their worst start to a season since 2001.
Angel McCoughtry scored 19 points and Jasmine Thomas added 17 for Atlanta (2-2).
Larkins had five points and five rebounds in overtime as Indiana outscored the Dream 14-9 in the final 5 minutes.
Indiana's offense managed just four points in the fourth quarter to match a franchise low. The Fever missed 12 straight shots from the field before January's reverse layup forced a 68-all tie with 1:57 left in regulation.
Atlanta, which won in double OT at Indiana last week on McCoughtry's 3 in the closing seconds, never led after she hit a 3 to make it 68-66 with 4:08 left in regulation.
The Dream committed 21 turnovers, leading to 27 points for Indiana.
Indiana was without forward Tamika Catchings, the 2011 WNBA MVP and 2012 finals MVP, for the fourth straight game, but the Fever got 14 points from Sydney Carter and 12 from Natasha Howard.
Sancho Lyttle finished with 15 points and Erika de Souza had 14 for Atlanta, which swept Indiana in the Eastern Conference finals last season.
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