Catchings' 3-pointer with 1:34 remaining in overtime put the Fever ahead for good, 75-74. On that basket, she surpassed Lisa Leslie as the WNBA's all-time leading scorer in the postseason.
The Fever will face top-seeded Atlanta or No. 4 Chicago in the conference finals.
Kara Lawson scored a season-best 20 points for the Mystics. Including the regular season, Washington lost five of its final six games.
Indiana won Game 1 by 78-73 at home on Thursday.
Briann January scored 13 for Indiana. Her two free throws with 19.7 remaining in regulation tied the game 66-66.