There was an even start to the match with the first scoring opportunity falling to Little Oakley in the 20th minute but the Shrimpers goalkeeper Brad Cook did well, saving with his feet.
Harwich came back with Joe Knight shooting over the crossbar and a little later seeing his effort diverted for a corner.
Little Oakley's danger man was proving to be their new striker Darren Mills, formerly of Ipswich Wanderers, and he was inches away from reaching a cross that fizzed across the goalmouth.
Seconds before the half time whistle, Mills gave Little Oakley the lead when he netted with a header from a well-placed corner kick.
With 15 minutes of the second half gone, Harwich equalised when Alfie Canning's pass found Luke Mayhew and his cross was neatly converted by Zac Elseidy, who was with Holland FC last season.

League fixtures announced: Shrimpers start at Wivenhoe

The Acorns were being driven on by dynamo captain and ex-Shrimper Rory Harman and Cook was called upon to make another good stop with the Shrimpers defence being tested.
Both teams used their substitutes as the pace of the game increased and it was Harwich's turn to create two really good chances. Firstly Canning, who was working his socks off, set up Ben Sargeant with the clearest chance of the match but with the goal gaping he shot the wrong side of the post.
Next Sargeant cleverly played Canning in but the home goalkeeper was alert and advanced to make an excellent block.
It was an exciting finish to an entertaining game in which both sides came close to claiming victory.
Harwich team: Brad Cook, Dan Keeble, Will Crisell, Jack Wood, Harry Tuck, Alfie Smith, Gareth Heath, Alfie Canning, Luke Mayhew, Zac Elseidy and Joe Knight. Substitutes: Danny Garrad, Ben Sargeant, Freddy Bethell, Tyler Sullivan, Brandon Rusby and Ewan Livingston (all used)

• The planned friendly between the Under-23s and Great Bentley on Saturday was postponed.