Keeper Murphy was then sent off for deliberate handball, with the decision paving the way for Charlie Adam, Ben Burgess and Alex Baptiste to seal the win for Ian Holloway's men, leaving Scunthorpe without a win at Bloomfield Road since April 2000.
They have also lost their last three games but will return to Lincolnshire wondering what could have been.
Blackpool, with two draws from their last two games, started well with Adam slamming a long-range drive just over, while at the other end Grant McCann scraped an effort wide for the Iron.
Scunthorpe's passing game was causing Blackpool a number of problems and had Hayes reacted better when he found himself well placed they could have opened the scoring.
As it was, the home side were the first to go genuinely close, as Billy Clarke bent an effort against the post after beating Rob Jones for pace.
Scunthorpe continued to threaten and Matt Sparrow was denied by Matt Gilks after breaking through, while Hayes should have done better with a free header from a corner.
Hayes, playing without his usual strike partner Gary Hooper because of illness, continued to cause problems and flashed a drive across the face of Blackpool's goal that Andrew Wright almost got on the end of.
Scunthorpe were by far the most dangerous of the two sides but were not able to make their dominance count before the interval came.
They nearly did four minutes after the restart, though, with Hayes twisting and turning before thumping a shot straight at Gilks.
Hayes finally got his reward 51 minutes in, collecting Grant McCann's precision pass before clipping the ball over the advancing Gilks for a picture book goal.
David Mirfin very nearly found a way through a crowded box to give the Iron a second goal, before the game turned on its head in the space of 11 minutes.
First of all, Evatt found himself unmarked at the back post to nod home Baptiste's cross for a second goal of the season a minute before the hour mark.
Then, George Friend, making his Iron debut, sold David Mirfin short with a backpass. Murphy came out of his area to provide cover and, after Baptiste robbed Mirfin of possession, the Republic of Ireland keeper automatically saved Baptiste's goalbound effort prompting referee Colin Webster to brandish the red card.
Debutant Sam Slocombe came off the bench to replace Murphy, but his first touch was to pick Adam's 64th-minute free-kick out of the back of the net - a delightful strike which would have left most goalkeepers with no chance.
Keith Southern then hit the bar for a rampant Blackpool, before an error from Slocombe allowed Burgess to convert from close range with 20 minutes remaining.
Slocombe fumbled Stephen Crainey's cross and Burgess was on hand to capitalise.
With Scunthorpe now beaten, Baptiste rubbed salt in their wounds with a 25-yard drive a minute from time, while Sparrow had a late goal ruled out for offside.