Rebekkah Brunson scored 16 points to help the defending champion Lynx bounce back from a double-overtime loss in Game 2 and win the best-of-3 opening round series.
Minnesota will host Los Angeles in the opener of the West finals Thursday night. The Sparks swept San Antonio in their series.
Sue Bird scored 19 points and Camille Little had 17 for Seattle.
The Storm had a chance to win it in the final seconds, but Lauren Jackson's turnaround jumper went off the rim.
Seattle, which won the championship in 2010, lost in the conference semifinals for the seventh time in eight years.
Minnesota never led by more than six points in the second half.
Trailing by four points, Bird made a 3-pointer to get the Storm to 73-72 with 35 seconds to play.
After Lindsay Whalen missed a leaner for the Lynx with 10.4 seconds to play it took Seattle 7 seconds to call a time out, leaving just 3.3 seconds to execute a final play.
With Minnesota leading by one point midway through the final period, Brunson and Whalen hit jumpers 33 seconds apart around a missed 3 by Bird to make it 69-64. Bird then answered with a 3 to pull the Storm to within two with 2:47 to play.
A baseline drive by Augustus put the Lynx up by four 30 seconds later, but Katie Smith answered with a long jumper. Taj McWilliams-Franklin scored in the paint to put the Lynx up 73-69 with 1:37 to play.
Both teams missed 3s before Bird, who shot 2 for 6 from beyond the arc, made one to pull the Storm within one.
Whalen was limited for much of the game after falling on her left wrist in the first quarter. She had the wrist heavily taped for the second half, but clearly favored using her right hand.
Augustus scored eight of the first 11 Lynx points to start the second half to give Minnesota a 47-41 lead, but Minnesota couldn't build on its margin. A jumper by Smith got the Storm to 56-52 at the quarter's end, and she hit a 3 to start the fourth.
Minnesota, which was just 6 for 30 from the field in the fourth quarter and two overtimes Sunday, shot 64 percent in the first quarter.
Moore scored 10 points during an 18-4 run to give the Lynx a 20-12 lead late in the opening period, but Minnesota started just 1 for 12 in the second.
Seven straight points by Little put the Storm in front 26-25.
Moore made a 3 with 20 seconds to play in the half to give the Lynx a 36-32 lead, but Tanisha Wright answered from beyond the arc just before the buzzer to get Seattle to 36-35 at the break.