After a defensive battle for most of the game, Bay FC's Asisat Oshoala got on the end of Penelope Hocking's cross in the 82nd minute, silencing the sellout crowd of 19,215 at Audi Field.
The play started when Alyssa Malonson whipped in a cross from the left that slipped all the way through to an unmarked Hocking on the far post. The substitute sent the ball back across the goal for Oshoala to finish with her first touch.
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Tara McKeown equalized three minutes later. The center-back, who converted from forward last season, picked off a Bay clearance, dribbled forward and finished into the lower left corner with a shot from the top of the 18-yard box.
It's the second time in league history that the go-ahead and equalizing goal were both scored after the 80th minute, with the result sending the Spirit to the semifinals.
While Rodman was held scoreless in the game, her cross forced the go-ahead goal six minutes into extra time. Bay FC defender Caprice Dydasco saw the ball late and accidentally redirected it into her ow net to give the Spirit the lead.
Both teams held firm defensively in the first half, with Bay FC having a slight edge in shots (7-5) in the first 45 minutes against a Spirit side that scored 51 goals in the regular season.
The game opened up after the first goal, and the Spirit ended with 21 shots. Bay FC goalkeeper Katelyn Rowland made five saves.
The Spirit (18-6-2) were hit with injuries to several key players this season but still finished in second place. Rookie Croix Bethune, who led the league with 10 assists, tore her meniscus in August. Andi Sullivan tore her ACL in October, and joint leading goal scorer Ouleymata Sarr has been out with a back injury since September.
Expansion team Bay FC (11-14-1) made a late surge and qualified for the playoffs in the last match of the regular season.
The Spirit, who won the club's first NWSL Championship in 2021, will host defending champions Gotham FC, which beat the Portland Thorns later on Sunday, in next weekend's semifinal.