The Essex visitors found the twin strike force of Hayes and Steve Torpey a real handful, despite a fine performance from skipper Kevin Maher.
Scunthorpe skipper Andrew Crosby had a solid game and admitted afterwards, "Southend were a good side, but we just found that bit extra."
After what appeared to be a nonchalant start, the game came to life with three goals in the final 15 minutes of the opening half.
Southend had not threatened at all, but they made the breakthrough after half an hour, when Wayne Gray made ground on the right and got round his marker to find Freddy Eastwood, who had acres of space to pick his spot and head home.
Gray then created another opening, but this time Jim Corbett was way off target.
Scunthorpe hit back with initially Torpey failing to find the net, but he compensated for that in the 25th minute, turning in Cleveland Taylor's cross at Darryl Flahavan's left-hand post.
The Iron capitalised with a second goal on the interval whistle, Lee Ridley's cross saw an error in the visitors rearguard and Hayes snapped up the opportunity.
Southend strove hard for an equaliser and Paul Musselwhite saved the home side with a flying stop from the energetic Eastwood, but there was little he could do to stop Corbett's 63rd minute goal, as he fired into the top of the net as the ball fell invitingly from a Scunthorpe defender.
That fired the home side to greater efforts and Hayes and Peter Beagrie went close, but they grabbed the lead for a second time when Hayes got the final touch to a Beagrie corner in the 72nd minute.
That signalled an assault from Scunthorpe and twice Flahavan had to fling himself across goal to deny the effervescent Hayes.