Daniel Arzani's goal in the 21st minute, combined with some goalkeeping heroics from Patrick Beach, had appeared enough to deliver reigning champions City a 1-0 win at HBF Park.
But Taggart equalised in the 90th minute to become the Glory's greatest ever ALM goalscorer.
"It means the world," the 32-year-old told Paramount Plus.
"Obviously grew up watching Damian Mori and Bobby Despotovski score goals here.
"To reach this number is special for me."
Until the goal, Taggart - who had been on a six-game goal scoring drought - had a nightmare evening in attack, peppering City's goal without reward.
Currently out of the Socceroos frame, Taggart conceded that sitting on 59 goals alongside Andy Keogh had weighed on his shoulders and his confidence had dropped.
"I didn't think I would be able to buy one tonight," Taggart joked.
Adam Griffiths' 11th-placed Perth (24 points) are winless in seven but sit just five points outside the top six, while City spurned their chance to leap to sixth.
Ninth-placed City (26 points) trail sixth-placed Macarthur (29), Central Coast (27) and Wellington (27), albeit with a game in hand.
One positive for Vidmar's charges is a promising outing from Arzani, who was overlooked for Australia's games against Cameroon in Sydney on Friday and Curacao in Melbourne the following Tuesday.
Arzani hadn't scored since joining City from Ferencvaros on loan in January but snagged his first goal back in City colours after in-form winger Marcus Younis stood up a defender and sent the ball into the box.
City striker Max Caputo knocked the ball down and Arzani was quickest to react, rolling it onto his left foot then coolly finishing into the bottom corner.
But after the goal, the best moments came through Perth, with Aziz Behich and the superb Beach thwarting Taggart multiple times.
Perth goalkeeper Matt Sutton denied Emin Durakovic and then Younis to keep Perth in the match in the 88th minute.
Taggart then found Jaiden Kucharski and wiggled into space to receive the ball back before firing home the equaliser.
Perth next travel to play Central Coast while City host Western Sydney.
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