Newcastle took the lead thanks to a wonder strike from Taggart midway through the first-half before the Wanderers level through a scintillating set-piece strike from Aaron Mooy right on the stroke of half-time.
Western Sydney skipper Michael Beauchamp put his side into the lead just after the hour mark when he was in the right place at the right time to deflect a Josh Brillante clearance into the Jets' net before Taggart snatched a share of the spoils when he poked home in the 90th minute.
The draw sees the Wanderers maintain second spot in the Hyundai A-League ladder while the draw arrests a mid-season slump for the Jets.
Newcastle were dealt a body blow on the eve of the game when marquee player Emile Heskey suffered back spams in the warm-up and was forced to sit out the match. Nicky Ward was promoted to the starting side to play alongside Taggart at the point of the Newcastle attack, with Josh Mitchell coming onto the bench.
Despite the setback the home side started brightly with Craig Goodwin and Andrew Hoole finding plenty of space on the wings and sending some dangerous crosses into the box.
Ward went close to opening the scoring in the 12th minute when Hoole sent a dangerous low-cross into the box but Western Sydney goal-keeper Ante Covic bravely dived in at the feet of Ward to snuff out a scoring chance.
Down the other end the Wanderers applied some sustained pressure with a series of corners but for the most part they were forced into hurried long-range attempts that sailed wide of the target.
The Jets continued to toil heartily and they duly opened the scoring in the 26th minute with a glorious thunderbolt from Taggart. Hoole took the ball in the midfield and weaved his way into Wanderers territory before being tackled by Matthew Spiranovic. The ball popped out to Taggart who unleashed a searing strike that found the top left corner of the net.
Newcastle went close to doubling their lead just after the half-hour mark when Goodwin skirted into the box from the left-wing and fired a shot at the near post that was parried away by Covic.
The Wanderers struck back right on the stroke of half-time with a scintillating long-range free-kick from Aaron Mooy, who curled a delightful 30-metre effort over the wall and into the top corner to send the teams to sheds locked at 1-1.
Taggart went close to grabbing a second goal just after the interval when he fired a vicious shot from an acute angle with Covic forced to tip the ball over the crossbar.
Newcastle club legend Joel Griffiths made his much-anticipated return to Hunter Stadium when he came on for Ward just after the hour mark, but it was the Wanderers who were celebrating when they took the lead just moments later.
A Wanderers corner resulted in a goal-mouth scramble with Jets defender clearing the ball off his line, but he only fired his kick into the shoulder of Western Sydney skipper Michael Beauchamp who had his head turned as the ball ricocheted into the net.
Wanderers substitute Labinot Haliti nearly sealed it for the Wanderers when he fired a powerful low shot through a crowded penalty box that saw Mark Birighitti pull off a fantastic diving save.
Taggart snatched a draw for the Jets in the final minute of the match following a corner that resulted in a goal-mouth scramble and Taggart poking home from close range.
Drama ensued even after the final whistle when Taggart was brought down in a heavy challenge by Covic and when Griffiths remonstrated with referee Ben Williams he was shown a red card for dissent.
Newcastle Jets 2 (Taggart 26, 90)
Western Sydney Wanderers 2 ( Mooy 45, Beauchamp 65)
Crowd 15,924 @ Hunter Stadium
