The keeper made one smart save from veteran Marcus Stewart, but was helped out by a defender when Stewart's overhead kick was blocked on the line and then by the crossbar in stoppage time in the first half when Stewart managed to beat him with a header.
Blackpool came out looking much brighter at the start of the second half and got the all-important goal in the 57th minute.
Wes Hoolahan got in a good ball from the right and went across the box to Andy Morrell, whose low drive flashed into the far corner of the net.
Blackpool's celebrations were checked two minutes later when their skipper Shaun Barker was sent off.
He had been booked in the 37th minute for a foul on Stewart and a second yellow was inevitable when he blocked Aaron Davies near the corner flag.
"I had only committed three fouls in the match and I thought both bookings were harsh,'' said Barker afterwards.
However, the Blackpool defence continued to do a magnificent job to record a fifth successive match without defeat.
Manager Simon Grayson said it was a "fantastic'' result at a very difficult venue.
His opposite number Russell Slade said: "We didn't make the most of our opportunities. Next week we're at home to Chesterfield and it is absolutely essential we win.''