Substitute Clayton, 17, had only been on the field 10 minutes when he tucked the ball home to put his side 3-1 ahead on aggregate in the 86th minute.
Ajay Leitch-Smith had earlier opened the scoring for the visitors before Neil Harris levelled for Southend in the second half.
Clayton's strike appeared to be enough but Chris Barker ensured a nervy final few minutes for the visitors when he headed Southend level on 88 minutes.
But Crewe, who won the first leg courtesy of Adam Dugdale's goal, held out to book a place in next weekend's final against Cheltenham or Torquay.
Southend, looking to reach a Wembley final for the first time in their history, threatened in the early stages with Bilel Mohsni testing goalkeeper Steve Phillips from long range and Sean Clohessy firing over.
However, Crewe stunned the home crowd in the 24th minute thanks to a superb strike from Leitch-Smith.
Ashley Westwood won the ball in midfield and fed Leitch-Smith, who still had plenty to do in the corner of Southend's penalty area.
But the 22-year-old striker turned back inside Clohessy, shifting the ball onto his right food before sending his shot arrowing across Shrimpers goalkeeper Cameron Belford and inside the far post.
Southend thought they had scored eight minutes later after Phillips spilled Ryan Hall's shot at the feet of Freddy Eastwood, but he was offside when he swept the ball home.
Moments later it was Belford's turn to blunder, gifting Crewe a chance to put the game to bed when his attempted clearance flew straight to Byron Moore.
The winger found himself clean through, just inside the area, but his composure deserted him as he shanked a shot embarrassingly high and wide, almost clearing the stand behind the goal.
Belford made amends either side of half-time, denying Leitch-Smith as he burst through again before diving to his left to keep out a fierce volley from Moore.
Southend must have known their luck was out when they were denied by the woodwork twice in as many minutes.
First Michael Timlin's shot from outside the box clipped the upright, and moments later Eastwood's low drive thumped the inside of the opposite post and rolled agonisingly across the goal-line to safety.
The hosts did haul themselves back into the tie just after the hour mark, substitute Harris profiting from another Phillips error to slide the ball home.
But as Southend poured forward they were undone on the counter-attack, with Clayton holding the ball up before rolling it inside Phillips' near post.
Barker immediately headed Southend level again three minutes from time but Crewe, who finished 11 points behind their opponents in seventh, are now just 90 minutes from promotion.