Elsewhere, Adelaide sit second after coming from behind for a 1-1 home draw with finals aspirants Canberra United.
City are nine points clear of second-placed Adelaide and 10 ahead of third-placed Victory.
Sydney sit last and 14 points outside the top six, their season slipping away with seven games left.
"Today was a big game because I did think we could still get in," Sydney coach Ante Juric told AAP.
"But we needed to win eight games in a row in my head, unless Western United or Central Coast lose six out of seven, or seven out of seven - and that won't happen.
"Mathematically we're there (alive), but yeah it's realistic that we won't get in.
"But again, we're going to work hard to get points and finish as high as we can.
"Yes, we're expected to be top of the table and things like that, and we're not. And I take that definitely on my shoulders.
"But if they (the players) keep working like that, next year they'll turn it around, next seven or eight games we'll get some results.
"So I'm proud but disappointed because we don't deserve to be where we are."
Sydney took a shock lead in the 13th minute at AAMI Park when City goalkeeper Malena Mieres passed forward to Laura Hughes under immense pressure and Hughes lost the ball, allowing Mackenzie Hawkesby to pounce and score.
City's equaliser arrived 24 seconds after half time.
Speckmaier won the ball just inside her own half and sprinted until just outside the 18-yard box before unleashing an unstoppable strike.
"Momentum is a big thing, and sometimes in these games, when it's really tight, you need your big players to stand up and do something special," City coach Michael Matricciani told AAP.
City skipper Rebekah Stott made a game-saving tackle on Amber Luchtmeijer in the 86th minute.
Three minutes later, Leticia McKenna brilliantly split open the Sydney midfield to find Lourdes Bosch, who slipped the ball forward for Bryleeh Henry to score the winner.
Natalie Tobin largely marked City star Holly McNamara out of the game, ahead of the striker linking up with the Matildas for the SheBelieves Cup.
"Tobin's been at a different level. I'm extremely surprised she hasn't had a look in with the Matildas," Juric said.
At Coopers Stadium, Canberra snatched the lead in the 45th minute when Adelaide goalkeeper Claudia Jenkins failed to properly clear a corner and Darcy Malone headed the ball inside the near post.
Adelaide continued to press for an equaliser and found it when Erin Healy brilliantly slipped through Fiona Worts, who squared it for Chelsie Dawber.
The striker burst forward and unleashed her seventh goal of the season from just inside the box.
On Sunday, Victory take on Central Coast, Brisbane host Western United and Perth take on Wellington.
