Yeovil had twice taken the lead through Gavin Williams and Jonathan Franks at Huish Park and looked to be on their way to their sixth win in seven matches.
The Iron looked down and out for much of the game, but the Glovers wasted a host of chances with top-scorer Andy Williams twice firing wide early on.
Gavin Williams smashed in a low free-kick on 30 minutes but Scunthorpe levelled eight minutes into the second half when Mark Duffy put Parkin clear.
Yeovil battled for the winner and looked to have got it when Franks slotted home following a good pass from fellow loanee Jonathan Grounds.
But Parkin popped up just at the right time to convert Andy Barcham's spilled shot and salvage a point for the visitors.