The tall striker opened Swindon's account with a spectacular goal three minutes into the second half and then salvaged a point with a late equaliser after Bournemouth had taken the lead.
Bournemouth almost snatched a victory in the dying minutes when substitute Jo Kuffour, whose introduction at half-time almost turned the match on its head, rattled the Swindon upright.
Corr, who had scored in Swindon's two previous Yuletide wins over Hartlepool and Yeovil Town, lit the fuse on a drab affair early in the second half.
Picking the ball up some 25 yards out, he picked his spot in the top right-hand corner with a gem of a curling shot to give Swindon the lead.
Soon afterwards, Reading loan striker Simon Cox had a potential second Swindon goal ruled out for handball.
It proved to be somewhat of a turning point as Bournemouth grabbed the initiative and, after 63 minutes, snatched the lead.
Warren Cummings fired in a low ball, teenager Sam Vokes saw his effort charged down, but Kuffour was on hand to fire Bournemouth's equaliser in off the underside of the bar.
Bournemouth laid siege to the Swindon goal and really ought to have been out of sight in the next ten minutes but missed a catalogue of chances.
Twice Alex Pearce went close, before Vokes had a shot saved by Swindon goalkeeper Petr Brezovan.
Substitute James Henry shot wide and then Vokes skied a shot over the bar when it looked easier to score.
Eventually Bournemouth's pressure paid off from a set-piece.
Brezovan turned a goalbound effort from Danny Hollands around the post from a corner but the flag-kick proved decisive.
Jason Pearce saw his shot rebound off Henry straight into the path of Vokes, who put Bournemouth 2-1 in front.
Bournemouth almost scored a third two minutes later when the impressive Max-Alain Gradel had a shot tipped over the bar.
But with eight minutes left, Swindon made Bournemouth pay dearly for their wastefulness when Cox hooked the ball across the face of the home goal for Corr to score at the far post.
In a dramatic finish, Bournemouth almost snatched the points but Kuffour saw his effort agonisingly strike the upright and rebound to safety.