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.
''We did a good job holding our composure down the stretch,'' Catchings said. ''When you look at it there are things that you're happy about and things you aren't happy about. Just continuing our quest to be a good team. We made some great defensive stops.''
Indiana finished 53 percent from the field, including 9 for 18 on 3-pointers.
Cappie Pondexter scored a season-high 33 points and Essence Carson added 14 for the Liberty (6-11), who have lost two straight and six of nine.
''Felt like we could have won the game,'' Pondexter said. ''We had a chance. It seems like we battle this team back and forth, playoffs, regular season, for the past three years ever since I've been in New York.''
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.
''It was kind of a playoff mentality, playoff atmosphere,'' Douglas said. ''We have kind of been able to learn from San Antonio to sustain a team's run and maintain our own run and come up with crucial baskets at the end. I'd much rather learn from a win than a loss.''
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.
''It was a hard fought game,'' Liberty coach John Whisenant said. ''Indiana's hard to beat at home or anywhere. We got back in and got a lead. They made the play at the end. Our team battled back and didn't get the win.''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.
The Liberty were playing their seventh straight game without second-leading scorer and rebounder Plenette Pierson (strained left knee) and the third in a row without leading rebounder Kia Vaughn (concussion).
- Tamika Catchings
- Indiana Fever
- Cappie Pondexter