Katie Douglas scored 18 points. Chiney Ogwumike added 16, and Montgomery had 15 to help the Sun (9-10) rebound from a 13-point home loss to the Shock on Thursday night.
After that loss, Douglas called out her Connecticut teammates.
"It's no fun losing," Douglas said. "I felt like we were definitely on a skid. I just implored them to have as much energy as we possibly could. We knew we could get the job done. We went on a six-game winning streak earlier so we knew we could play at a much higher form. We took this like it was our last game."
Sun coach Anne Donovan was pleased Douglas challenged the other players.
"I'm not surprised (Katie) did that," Donovan said. "It's one thing for the coaches to keep pointing things out, it's something different altogether for (Katie) to do it. She knows it's the second half of the season and if we want to get to the playoffs, we have to step up."
Skylar Diggins led Tulsa (7-11) with 30 points, her sixth game this season with 25 or more points. Glory Johnson had 13 points and 11 rebounds, Odyssey Sims added 14 points, and Courtney Paris had 12.
"I don't know that we limited Skylar or Odyssey," Douglas said. "They are obviously a major part of their offense. They are quick with the ball and Tulsa runs a lot of isolation players for them. Tonight, we did a better job team-wise on being in the right spots (defensively). At times they made some shots, but I think our defense was there compared to Thursday."
Connecticut built a 12-point first-half lead, but the Shock rallied to tie it Diggins' driving layup with 24.3 seconds left. Diggins was fouled on the play by Montgomery, but missed the free throw. Montgomery made up for the defensive miscue with the winning basket.
"A lot of our opportunities came up empty early and kind of set the tone for us," Tulsa coach Fred Williams said. "We hung in there and fought through some things that didn't go our way. We were able to tie the game there at the end. This was probably one of the most physical games we've had all year."