Cooper scored 20 points, including five in the last minute, as the Comets held off the New York Liberty, 59-52, in Game 1 of the WNBA finals on Thursday night.
"I always have stepped it up for the playoffs," Cooper said. "The regular season is great and fine, but the playoffs is where you're supposed to bring your 'A' game. And that's what I'm doing."
Cooper, 37, shot just 7-for-23 but made some of the most important baskets of her career late in the game. The Comets can become the first professional sports team to win four consecutive championships since the NHL's New York Islanders in 1980-83.
"We're fighting to make history," Cooper said. "I'm on a mission because we have made a lot of sacrifices throughout the season, and deserve to fight for this fourth one. And I'm on a mission because that's what a professional athlete does at this time of the year â€“ elevate her game."
Tina Thompson added 15 points and Sheryl Swoopes had 12 for Houston, which stopped the Liberty's 13-game winning streak at Madison Square Garden and sent the best-of-3 series to the Compaq Center, where the Comets have lost just once in 12 postseason games.
Game 2 is Saturday at Houston, with Game 3, if necessary, there on Sunday.
"We're not going down there to lose, I can tell you that," Liberty guard Becky Hammon said. "We're going down there to win."
Tari Phillips of New York had 24 points on 10-for-19 shooting and grabbed 15 rebounds in a game deemed by many Liberty players as a must-win.
After a sloppy first half in which both teams struggled to score, Houston and New York turned it on in the second half.
The Comets opened up a 52-42 lead on Swoopes' free throw with 7:40 remaining, but the Liberty went on a 6-0 run.
Phillips made a layup at 7:21 to make it 52-44. Tamika Whitmore made two foul shots at 4:36, and Phillips put back Vickie Johnson's miss to make it 52-48 with 4:03 left.
The teams went scoreless until 52.3 seconds remained, when Teresa Weatherspoon made two free throws after getting fouled by Swoopes, to make it 52-50.
Cooper followed with a tough running layup with the shot clock winding down and was fouled by Sue Wicks.
"Cynthia Cooper made one of the greatest shots you will ever see," Houston coach Van Chancellor said.
Cooper, who finished 7-of-23 from the field, made the foul shot to give the Comets a 55-50 lead with 26.4 left.
"She's what you call a champion," Weatherspoon said.