Southend took the lead midway through the first half, as Ben Coker found space down the left and his low cross found Hunt in the box. His strike was saved by Ben Alnwick but it fell to the feet of Adam Barrett and the defender scrambled the ball into the back of the net.
It could have been two soon after, with David Mooney getting on the end of a good passage of Southend passing play but his low drive was saved well by Alnwick.
The second came after half time from another Coker cross, this time from a free kick which was met by Hunt and his glanced header helped guide the ball past Alnwick to give Southend a commanding lead.
The win moves Southend up to 15th while Peterborough drop below the Seasiders and are just a place above the relegation zone in 19th.