FC Clacton took the lead in the 27th minute with an alert finish from Douglas Herrington.
Harwich's best effort came from a fierce drive from an angle by Jaidan Smith that went into the side netting but generally the Shrimpers were not at their best in this half.
The Seasiders looked far better than a team languishing at the bottom of the league table and deservedly increased their lead in the 37th minute and again it was a well-taken goal, this time netted by Aron Jones.
Clacton continued to play well after the break but Harwich were now getting their game together.
First-team game abandoned due to power failure
With 20 minutes remaining, the Shrimpers reduced the arrears with a well-worked move, Freddy Bethell neatly heading home from Cody Harrison's well-placed cross.
With less than 10 minutes left, Harwich won a penalty kick and Harrison (pictured) calmly struck the equalising goal.
It was a nail-biting finish with both teams going for a winner. Harwich threatened with some dangerous corners whilst with almost the last kick, Clacton had a shot go agonisingly the wrong side of the post.
Harwich team: Wayne Chilvers, Archie Corner, Harry Tuck, Tony Clarke, Alex Pryke, Batuhan Macit, Freddy Bethell, Archie Rogers-Bell, Jamie Beecham, Cody Harrison and Jaidan Smith. Substitutes: Rory Breen, Solomon Gfriffiths, Jack Milne and Joseph Simmons.