Southend's Damian Scannell unleashed a curling right-foot shot that went just wide of the post before Nicky Bailey rifled in a 30-yard effort that Joe Lewis did well to hold.
The Posh blew a great chance when Chris Whelpdale's cross from the byline flashed across the face of goal and beyond the outstretched leg of Craig Mackail-Smith.
Peterborough had the final say of the half when Charlie Lee blasted a well-struck 25-yard shot inches wide of a diving Steve Mildenhall.
The second half was a fairly scrappy affair until Clarke's goal as Southend skipper Adam Barrett headed straight at Lewis and a Bailey shot was deflected just wide.
Aaron Mclean had a great chance for Posh but his shot from 14 yards was parried for a corner by Mildenhall.
Southend upped the pressure and were rewarded when debutant Dan Harding's corner from the right dropped to Clarke and he lashed the ball into the roof of the net from six yards.