Katie Douglas scored 20 points and Shavonte Zellous added 12 as the Fever (10-6) squandered a 12-point lead and trailed by four in the final minutes before rallying.
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Indiana finished 53 percent from the field, including 9 for 18 on 3-pointers.
Trailing 73-70 midway through the fourth quarter, the Liberty scored seven consecutive points to take their biggest lead. Leilani Mitchell made 3 to tie the score, Pondexter hit a technical free throw called on Indiana's Briann January for arguing and then Pondexter made a 3 to put New York up 77-73 with 3 1/2 minutes to go.
Catchings came back with a 3-pointer nearly a minute later and hit another one with 1:53 remaining to give the Fever a 79-77 lead.
Pondexter hit a tying jumper, and Douglas and Pondexter traded 3-pointers 14 seconds apart to leave the score tied at 82 with 35.5 seconds to go.
Indiana passed inbounds with 17.5 seconds left in the game and 6 seconds to go on the shot clock. The ball went all the way to the backcourt, where January tracked it down, hustled upcourt and missed a desperation shot. Catchings rebounded and was fouled. She made both free throws to put Indiana ahead.
New York had one last chance, but January stole the ball from Kara Braxton, then Indiana came up with possession after a scramble and ran out the clock.
Indiana led 52-43 at halftime after shooting 61 percent from the field.
New York cut the margin to 66-61 early in the fourth quarter, and Alex Montgomery's 3-pointer made it a 4-point game. A pair of free throws by Nicole Powell cut Indiana's lead to two, and the Liberty tied the game at 70 on a fadeaway by Pondexter.