Dagenham took just four minutes to open the scoring through Paul Benson and capped a marvellous high-tempo performance at Victoria Road with five more goals.
Scott struck four in the space of 34 minutes with Benson adding another as the Daggers made a mockery of Morecambe's fourth-placed finish in the table.
John Still's side will now head to Christie Park on Thursday evening knowing that only a remarkable comeback from the Shrimps can stop them reaching Wembley.
Sammy McIlroy's visitors were never in the game and the former Manchester United midfielder faces a difficult task to rouse his side for the home leg - the final game at their old stadium.
Danny Green had already caused chaos with a couple of long throws before the Daggers grabbed a fourth minute lead.
Green's throw was only half-cleared and Abu Ogogo lobbed the ball back in to Jon Nurse at the far post who powered in a header.
His effort was well saved by Barry Roche but the ball ran free for Benson to tap in to an empty net.
The noisy away fans were silenced but not for long, as the Shrimps came close to an instant response.
A long ball forward was chested down by Garry Hunter for veteran Paul Mullin to strike on the half-volley but Tony Roberts spread himself to make a vital save.
Scott was next to threaten for the hosts with a header which looped over the crossbar, before the striker did double the lead in the 35th minute.
Roche was the villain as he scuffed his goal-kick horribly to the feet of Scott on the halfway line. The forward easily outpaced Jim Bentley to run in on goal and drive home a powerful left-footed strike.
Green then dragged an effort wide as Morecambe struggled to get to grips with the tempo of the hosts' attack.
McIlroy cannot have been happy with his side's tepid showing, and they started the second period in much brighter mood.
Mark Duffy chased down a lost cause and crossed for Laurence Wilson to fire wide, but the Daggers soon had a third in the 48th minute.
Still had seen two decent penalty shouts waved away in the first half but it was third time lucky as Green was tripped.
Captain Mark Arber saw his shot saved and Scott hit the post with his follow up, before finally scoring from inside a crowded goalmouth.
Scott had his hat-trick in the 54th minute. Green was again involved, swinging over a dangerous corner from the right which Scott headed past Roche.
It was 5-0 in the 66th minute after more woeful defending. Right-back Andy Parrish made a mess of a header to present Benson with the simple task of lashing past Roche at his near post.
The home fans could barely believe their eyes and the scoring was not yet complete.
Scott grabbed his fourth in the 69th minute when he seized on more indifferent defending to run in from the left and clip the ball into the far corner.