Canberra (13 points), a former league powerhouse who have been fighting for their survival in recent years, have beaten Perth Glory 3-0, Melbourne Victory 3-1, Sydney FC 2-0 and City inside seven rounds.
The Victory (12 points) are second after claiming a hard-fought 1-0 win over Adelaide United on Saturday evening.
Newcastle (10 points) bounced back from an F3 derby thumping to make light work of Brisbane, winning 3-0 to jump to third.
Canberra goalkeeper Sally James denied Holly McNamara in the early minutes at McKellar Park.
Then, in-form United made the contest their own and handed City their first home-and-away season loss in 31 games.
The hosts broke through in the 52nd minute when Nanako Sasaki lofted a ball to the back post and Emma Hawkins powered home a bullet header.
Seven minutes later, Heyman tapped home from a wonderful build-up from Sasaki and Hayley Taylor-Young.
McNamara got a goal back from the penalty spot after substitute Aideen Keane was brought down by Teagan Bertolissio, but it proved too little, too late.
"I don't think we deserved even a point today," City skipper Rebekah Stott told Paramount+.
"We need to be so much better."
At AAMI Park, Melbourne Victory were without Grace Maher and Zoe McMeeken, while Adelaide missed Matilda McNamara and Fiona Worts (overseas).
In the opening minutes, United goalkeeper Claudia Jenkins made a top save to deny Rhianna Pollicina a spectacular long-range goal.
Adelaide's Erin Healy forced a good save from Courtney Newbon in the 28th minute and a superb one-handed save with a fierce strike in the 41st.
The home side broke through in style in the 50th minute.
Holly Furphy's cross was cleared straight back to her and the attacker, who coach Jeff Hopkins said was "on a different level" had the presence of mind to cut it back for Rachel Lowe to slam in.
Adelaide coach Theo Tsiounis later confirmed Influenza A had ripped through his squad ahead of the game.
Earlier at the No.2 Sportsground, in-form striker Melina Ayres opened the scoring with an audacious 32nd-minute goal.
Ayres brilliantly brought down the ball, spun away from a defender and deftly turned a left-footed strike inside the near post.
For Newcastle's second, Kelli Brown won a penalty when she was brought down by Leia Varley, then dispatched the spot kick into the top corner.
The Jets sealed all three points in the 71st minute when Chloe Lincoln fumbled India Breier's long-range strike into her own net.
The Roar, who have lost skipper and Matildas stalwart Tameka Yallop (hamstring surgery) until late in the season, couldn't find a goal themselves.
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