An early own goal from Pilgrims defender Sonny Bradley put the Shrimpers in front at Roots Hall.
But Edwards' 62nd-minute equaliser ensured the game ended all square.
Southend - beaten 5-0 at Rotherham in their previous outing - bossed the majority of the first half and took the lead when Jermaine McGlashan's right-wing cross was diverted into his own net by Bradley.
The Shrimpers remained on top with Ryan Leonard shooting inches over from 20 yards and Edwards almost putting past his own goalkeeper when he stabbed a left-wing cross from Stephen Hendrie wide of the left post.
But, following a double substitution at the break, Plymouth improved at the start of the second half with Nathan Blissett having a low shot smartly saved by Mark Oxley.
The Pilgrims stayed on top and equalised in the 66th minute when Edwards headed home Graham Carey's left-wing corner before Oxley brilliantly denied Carey late on.
Match report supplied by the Press Association.
Match ends, Southend United 1, Plymouth Argyle 1.
Second Half ends, Southend United 1, Plymouth Argyle 1.
Attempt blocked. Stephen Hendrie (Southend United) right footed shot from outside the box is blocked.
Corner,  Southend United. Conceded by Jake Jervis.
Corner,  Southend United. Conceded by Ryan Edwards.
Corner,  Southend United. Conceded by Sonny Bradley.
Attempt blocked. Ryan Edwards (Plymouth Argyle) right footed shot from the centre of the box is blocked.
Michael Timlin (Southend United) is shown the yellow card for a bad foul.
Foul by Michael Timlin (Southend United).
Lionel Ainsworth (Plymouth Argyle) wins a free kick in the defensive half.
Attempt missed. Stephen McLaughlin (Southend United) left footed shot from outside the box is just a bit too high.
Stephen McLaughlin (Southend United) wins a free kick in the defensive half.
Foul by Yann Songo'o (Plymouth Argyle).
Corner,  Plymouth Argyle. Conceded by Mark Oxley.
Attempt saved. Graham Carey (Plymouth Argyle) right footed shot from outside the box is saved in the top right corner.
Substitution, Southend United. Stephen McLaughlin replaces Jermaine McGlashan.
Foul by Michael Kightly (Southend United).
Ryan Edwards (Plymouth Argyle) wins a free kick in the attacking half.
Attempt saved. Michael Kightly (Southend United) left footed shot from the centre of the box is saved in the top centre of the goal.
Jermaine McGlashan (Southend United) wins a free kick on the left wing.
Foul by Antoni Sarcevic (Plymouth Argyle).
Corner,  Plymouth Argyle. Conceded by Stephen Hendrie.
Attempt blocked. Antoni Sarcevic (Plymouth Argyle) right footed shot from the right side of the box is blocked.
Corner,  Southend United. Conceded by Graham Carey.
Marc-Antoine Fortuné (Southend United) wins a free kick in the attacking half.
Foul by Antoni Sarcevic (Plymouth Argyle).
Corner,  Southend United. Conceded by Gary Miller.
Attempt blocked. Theo Robinson (Southend United) right footed shot from the centre of the box is blocked.
Marc-Antoine Fortuné (Southend United) wins a free kick in the defensive half.
Foul by Gary Miller (Plymouth Argyle).
Substitution, Southend United. Theo Robinson replaces Simon Cox.
Corner,  Southend United. Conceded by Gary Miller.
Ryan Edwards (Plymouth Argyle) is shown the yellow card for a bad foul.
Jason Demetriou (Southend United) wins a free kick in the defensive half.
Foul by Ryan Edwards (Plymouth Argyle).
Goal!  Southend United 1, Plymouth Argyle 1. Ryan Edwards (Plymouth Argyle) header from very close range to the bottom left corner. Assisted by Graham Carey with a cross following a corner.
Corner,  Plymouth Argyle. Conceded by John White.
Attempt blocked. Graham Carey (Plymouth Argyle) right footed shot from the left side of the box is blocked.
Foul by Marc-Antoine Fortuné (Southend United).
Antoni Sarcevic (Plymouth Argyle) wins a free kick on the left wing.
Ryan Edwards' second-half header secured Plymouth Argyle a draw at Southend United in League One.