Paul Mullin's double was the difference as Wrexham swept Marine aside at the Optimum Pay Stadium
Phil Parkinson's side put right the wrong's of Saturday's initial tie with an assured performence in south Cheshire that smothered any chance of a cup upset.
Wrexham began as they would continue to go on, in control of the tie. However, Marine did have the first oppurtunity as Niall Kengi forced Christian Dibble into a smart stop after just five minutes.
Other than that, Wrexham were bright in their attacking intent with quick distribution from Dibble leading to Liam McAlinden winning a corner down the right.
The opening goal almost came on 14 minutes as Dior Angus fed through McAlinden who's pullback was inches away from finding Mullin at the far stick.
On 21 minutes, Mullin did get his chance. The forward broke down the left before cutting inside and glinding a wonderful effort into the bottom right corner to give Wrexham the advantage.
Marine tried to respond but Kengi could only blast over in the box and David Raven couldn't get a clean connection following a corner.
Half-Time: Wrexham 1-0 Marine
The second half began in perfect fashion for Wrexham, as Mullin was sent through one on one before rounding the goalkeeper and doubling the lead.
Moments later he'd almost complete a hatrick, with an effort cleared off the line with Wrexham looking to kill the tie.
Shaun Brisley almost had a debut goal as he put a header inches wide, whilst Jarvis had a free-kick batted away before Mullin's rebound was halted.
Marine found it more and more difficult to get themselves back into the tie, and almost found themselves dead and buried on 69 minutes as Mullin - in full form - lobbed the goalkeeper from 30-yards, but his effort went over the bar.
Wrexham were comforable and saw the game out, and now travel to EFL League Two Harrogate Town in the First Round Proper.
Wrexham Line-Up: Dibble, French, Hayden, Brisley, Reckord, Tozer, Davies, McAlinden, Jarvis, Mullin, Angus
Subs: Szczepaniak, Lennon, Cleworth, Hosannah, J.Jones, Ponticelli, Bickerstaff
Marine Line-Up: B.Passant, Solomon-Davies, Hayde, Howarth, Shaw, Raven, Watkinson, Doyle, Wignall, Barrigan, Kengi
Subs: Roberts, H.Passant, McNally, Devine, Reilly, Lynch, Cummins
Referee: David Richardson
Man of the Match: Liam McAlinden
Images: Barry Betts