Harwich started well and took the lead in the 12th minute with a smart move started by goalkeeper Brad Cook's long kick. Reece Harte's delivery into the box was good, Oakley McNair nudged the ball back across goal and new signing James Letts neatly netted.
The Shrimpers had so many players unavailable that it must have been a headache for manager Matt Carmichael but he put together a determined squad with a system that enabled Harwich to hold their own.
Great Wakering tested the Harwich defence with dangerous long throw-ins and won corner kicks from which their tall defenders came forward to threaten.
Following more good work by Letts, McNair, playing in midfield, sent a low shot just wide of the Rovers goal.
With 28 minutes gone Harwich were undone when Taylor Legg crossed into the Shrimpers goalmouth and in the ensuing scramble in the six-yard box Jack Dickinson equalised.
It was nip and tuck up to half time with Reece Harte twice sending dangerous crosses into Rovers goalmouth, and McNair getting back well to thwart the speedy Legg when he broke through the Shrimpers reargauard.
Harwich had done well to go in on level terms at the break but the second half proved to be a real challenge for them on their return to this level of football.
When Rovers' big striker Alex Teniola broke through and had a great chance, Cook was perfectly positioned to save his shot.
The Harwich defence now faced relentless pressure with the ball coming back at them and with 59 minutes gone, Great Wakering took the lead when Shaye La-Rose crossed for Harrison Topliss to volley home.
Harwich youngster McNair did well to provide Mayhew with a half chance but his snap shot on the turn went over the crossbar.
Rovers continued to press and central defender Charlie Canham saved Harwich at the expense of a corner kick and then Cook acrobatically palmed the ball away.
With the game now entering the last 10 minutes, Harwich had survived Rovers onslaught without conceding again and sensed their opportunity to snatch a draw. A chance came when Luke Spurling was fouled and from Max Long's free kick to the far post, Dan Keeble was just unable to make the conversion.
Then came Rovers' late third goal that ended the Shrimpers hopes when Topliss squared the ball to Igli Metalia who, from 30 yards out, rocketed his shot into the net.
Harwich team: Brad Cook, Tom Watkins, Reece Harte, Dan Keeble, Charlie Canham, Alfie Eldridge, Tyler Sullivan, James Letts, Oakley McNair, Alfie Canning and Luke Mayhew (captain). Substitutes: Greg Rodger, Luke Spurling, Max Long (all used) and Keelan Milburn (not used).