Elliott put the visitors in front after 80 minutes when he diverted the ball past Chris Neal and into the bottom corner.
The Pilgrims’ win was sealed moments later after Kyle Morrison hacked down Jake Wright Jnr inside the penalty area, leaving Elliott to step up and convert.
Fylde boss James Rowe had named an unchanged side from the final day 1-0 victory over Leamington FC, with Bobby Jones earning a place on the Coasters’ subs’ bench.
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Neither of the two teams had established real control after a fast-paced start to proceedings, but the first chance of the game fell for Boston and Elliott.
He latched onto a deflected shot from the edge of the area and poked the ball towards goal, but Neal was equal to it at his near post.
Fylde then started to get their foot on the ball as the game approached the 10-minute mark, which led to Will Hatfield winning a free-kick on the edge of the area.
Nick Haughton stepped up and dipped the ball inches over Marcus Dewhurst’s bar.
The Pilgrims had enjoyed most of the possession in the game, looking to make the Coasters work hard.
When Danny Philliskirk was dispossessed in the middle of the park, Elliott was allowed to drive at goal but he struck wide of goal in the process.
The final chance of the half would fall to Tom Walker after Danny Whitehead set the ball for him.
However, he flashed a right-footed strike over the Boston bar as half-time arrived with the game goalless.
Boston looked to apply pressure from the start of the second half and were awarded a free-kick when Connor Dimaio was brought down under pressure from Philliskirk.
Shane Byrne lifted the set-piece over the Fylde wall and forced Neal into a superb fingertip stop.
It was the away side who were on top, forcing the Coasters into some gritty defending.
They also forced Neal into another unbelievable save when he sprung across his line to palm away a rasping Elliott strike.
Boston eventually made their pressure count with 10 minutes to go as a dangerous ball into the box was turned in by Elliott at the near post.
Boston’s place in the promotion play-off final was then all but sealed as Morrison was penalised for a foul on Wright Jnr, which ended with Elliott stepping up and converting past Neal.
Fylde substitute Stephen Dobbie looked to at least pull one back in the dying embers of the game.
He bent an effort towards the bottom corner but Dewhurst managed to watch the ball go past his post.
AFC Fylde: Neal, Morrison, Davis, Whitmore, Walker, Conlan (Burke 68), Philliskirk, Hatfield (Whitehead 39), Haughton, Osborne, Taylor (Dobbie 88). Subs not used: Jones, Tollitt.
Boston United: Dewhurst, Garner, Shiels, Green, Ferguson, Dimaio, Byrne, Abbott, Seriki, Massanka (Wright Jnr 59), Elliott. Subs not used: Duxbury, Thanoj, Sault, Preston.