The first half saw both sides struggle to create chances and was most noticeable for the replacement of the injured Ian Evatt by the Latvian international Kaspars Gorkss and a dreadful challenge by visiting defender George Elokobi on Barker which could have earned him more than the yellow card he eventually received.
Blackpool came out strongly after the break and forced Aidan Davison into his first really tough save seven minutes after the break when a David Fox effort from the edge of the area was turned around the post.
But Davison was helpless when the resulting corner, taken by Fox, was flicked on by Gorkss for Andy Morrell to fire home from point-blank range at the far post.
Blackpool threatened to take a firm grip on the game and Davison again had to be on his guard to stop a Keith Southern effort just before the hour mark.
But the Seasiders were to regret the profligacy in front of goal when visiting substitute Jamie Guy was hauled down just outside the area.
Yeates curled the resulting free-kick around the Blackpool wall and beyond the clutches of keeper Paul Rachubka.
That left the home side rocked but they regained their composure and began to threaten as the match ran towards its conclusion.
With just six minutes left on the clock, another Fox corner found Barker at the far post and the former Rotherham man headed home what he thought was a likely winner.
But Blackpool should know better than to count their chickens and, for the second time in five days, they saw three points turn into one thanks to a late effort from the visiting side.
Yeates took advantage of another foul on Guy with a goal that was a virtual carbon copy of his first.