The Danish international central defender headed home a 90th minute equaliser - just five minutes after Candido Costa had fired Derby ahead.
Costa's first goal for Derby following his arrival on a season-long loan deal from FC Porto looked to be good enough to earn County a deserved win.
They had dominated the game for long spells only to be denied by four stunning saves from goalkeeper Russell Hoult, who starred against his former club.
He twice saved from Marcus Tudgay in the first-half and then frustrated Lee Morris and Luciano Zavagno in the second period.
But he was powerless to prevent Costa from firing Derby into a deserved lead.
The impressive Morris cut in from the left wing and weaved his way into the Albion area, before the loose ball broke for Costa who drilled home his shot from20 yards.
His strike set the scene for a stunning finale, which was capped when Gaardsoe struck.
A spell of Albion pressure earned them a corner that Jason Koumas floated into the box, with Rob Hulse heading the ball goalwards and Gaardsoe forcing it home from close range, to grab his second goal for the club since his £520,000 summer move from Ipswich Town.
The stalemate continued Albion's poor run of form at The Hawthorns and they have now failed to win at home in the league since the 1-0 win over promotion rivals, Norwich City, on October 18.
They have lost one and drawn five of the next five home matches - taking only five points from a possible 18.
While Derby should have taken all three points the draw did allow them to extend their recent good run, that has seen them beaten just once in their last seven games.