May opened the scoring after 13 minutes with a near-post header and then set up an opportunity for Hooper to make it 2-0 just six minutes later.
Scot McGleish reduced the arrears for Northampton after 25 minutes when he headed home a left-wing cross from Liam Davis.
Scunthorpe restored their two-goal advantage after 32 minutes when Hooper was left unmarked at the far post to head home a right-wing corner from Martyn Woolford for his 15th goal of the season.
The home side looked to have got the points all sewn up when May made it 4-1 with his second goal of the game in the 51st minute, after goalkeeper Chris Dunn had only half-blocked a shot from Woolford.
But Northampton struck back immediately with Giles Coke flicking a close-range shot past goalkeeper Joe Murphy to reduce the arrears to 4-2 in the 52nd minute.
Five minutes later midfield man Danny Jackman forced his way into the box to make it 4-3, beating Murphy at the second attempt.
Suddenly the nerves were jangling in the Scunthorpe defence and both Jason Crowe and Leon Constantine rattled the woodwork as the Cobblers searched for an equaliser.
At the opposite end Dunn twice denied Hooper a hat-trick with good saves, before the visitors finally got back on level terms with an 85th-minute equaliser which Jackman scored direct from a corner, curling the ball in from the right.
There was more drama in stoppage time when Jackman then popped up on his own goal-line to prevent Ian Morris snatching a last-gasp winner for the home side.