Seattle held Sparks star Candace Parker to just two points in the second half to overcome a 16-point deficit.
The 85-77 win gave the Storm just their second road win of the season and a 4-0 series sweep against the Sparks.
Parker, whose return has helped turn the Sparks' season in the right direction, finished the night with 12 points and 10 rebounds.
After going into halftime down 51-35 and facing its largest deficit of the night shortly after, Seattle outscored Los Angeles 50-29 in the second half. That included a 26-13 advantage in the final quarter.
"I don't even remember what I talked about at halftime. This is a group that analyzes itself pretty well," Storm head coach Jenny Boucek said. "A lot of the time, they say the things that they needed to say before I even get in there. That's a tribute to the humility in the leadership of our team and how close they are with one another and how much they're studying the game together.
"They've gotten to a point where they know when things aren't going well and what we need to do. I give them a lot of credit for continuing to fight and fight together," Boucek added.
Prior to the four-minute mark of the final quarter, the Storm (6-17) led the Sparks (7-16) by just one point all game at 3-2.
Seattle immediately responded to its largest deficit with a 14-6 run to pull within 49-57 with 4:07 remaining in the third quarter. Continuing the momentum, the Storm ended the quarter on a 10-4 run to head into the final period down just five.
"We have a game plan each game, and we always stick to it," Storm guard Sue Bird said. "Even if (the Sparks) were picking us apart in the first half, we stuck to our game plan and never stopped playing. It wasn't one thing particularly that changed the game. We just never stopped playing."
Seattle took the 72-71 lead, and took it for good, with four minutes left to play on a jumper by Bird.
Crystal Langhorne led the Storm with 18 points while Bird, Jewell Loyd and Kaleena Mosqueda-Lewis each had 15. Mosqueda-Lewis had the 3-pointer to tie the game at 66 with 7:07 remaining in the final quarter.
The Sparks agreed it was the team's energy that changed between the first and second halves. Head coach Brian Agler said there were 50-50 balls his team didn't get that, "when the game's in the balance ... are the difference makers."
Parker agreed the team's lack of energy meant they weren't "going to score offensively or get stops on defense."
"It was just disappointing. We didn't play hard enough," Sparks forward Jantel Lavender said. "(Seattle) just out-worked us in the second half ... (The Storm) just came out hungrier than we were. They were executing. They were playing some mismatches and were pretty much doing whatever they wanted to."
Lavender led the Sparks with 22 points. Nneka Ogwumike added 16.