Liam Marshall's hat-trick for Wigan looked to be in vain as Warrington fought back to seize the lead late on.
His treble built up an 18-6 lead but scores by Stefan Ratchford and Tom Lineham brought Warrington within two.
Jack Hughes then crossed for the Wolves as they went ahead but Burgess' try drew the reigning champions level and George Williams missed the conversion.
In a game of high drama even if it was low on quality, there was even a mini-brawl involving Kurt Gidley and Michael McIlorum as tensions frayed in the second half.
Wigan captain Sean O'Loughlin was perhaps fortunate to stay on the field when he high-tackled Gidley.
After the one-sided nature of the opening two games, this meeting of last year's Grand Final opponents produced a genuine contest, even if it was more of a defensive arm wrestle than a high-calibre affair.
O'Loughlin was talismanic for Wigan in the first half, providing a looping pass for Marshall's opener and may even have created another but his scything break was stopped by scrambling defence.
And it was the England captain's accurate and towering kick that Burgess leaped to collect in the left-hand corner to touch down and deny Wolves the win.
Neither coach was happy with the result but the fans went home satisfied after a proper tussle at St James' Park.
Wigan Warriors: Tierney, Davies, Forsyth, Burgess, Marshall, Williams, Woods, Nuuausala, McIlorum, Sutton, Isa, Farrell, O'Loughlin.
Replacements: Tautai, J. Tomkins, Wells, Field.
Warrington Wolves: Ratchford, Russell, Hughes, Atkins, Lineham, Brown, Gidley, Hill, Clark, Cooper, Jullien, Westwood, Westerman.
Replacements: Crosby, Philbin, Dwyer, G. King.
Referee: Ben Thaler (RFL)
Joe Burgess scored a dramatic last-minute try as Wigan Warriors drew with Warrington Wolves at Magic Weekend.