18-year-old forward Nick Powell smashed a stunning volley into the net from 20 yards out to give Steve Davis's side a deserved lead on 15 minutes.
Cheltenham dominated large swathes of the match from that point onwards, but were undone eight minutes from time when Byron Moore slipped the ball into the net from Ajay Leitch-Smith's pass to kill off the match with goalkeeper Scott Brown left with no chance for a second time.
The victory marks an astonishing transformation in Crewe's fortunes since Davis replaced iconic manager Dario Gradi - the club's director of football - with Crewe 18th in League Two and facing a potential relegation scrap back in November.
They have embarked on an unbeaten run of 19 matches in securing promotion via the play-offs. They have suffered only four defeats in 32 games under Davis, whose biggest battle during the close season may be in keeping several of his younger players at the club ahead of the League One campaign.
Mark Yates's Cheltenham have only themselves to blame for failing to take the chances that came their way on a boiling day at Wembley in which drink breaks were needed in both halves.
Jeff Goulding hit the bar a couple of minutes after Powell's opening goal before he lifted the ball over under pressure from Adam Dugdale.
Powell saw a shot swerve narrowly wide of the target and Kelvin Mellor headed over amid Cheltenham's period of dominance, but the Crewe goal was leading a charmed life before half-time.
Crewe goalkeeper Steve Phillips tipped a Goulding header over the bar minutes before the break with Kaid Mohamed hammering a shot over the bar from close range. Steve Elliott's header was then cleared off the line by Powell before Ashley Westwood brilliantly blocked Mohamed's shot on the line.
All roads continued to lead to Crewe's goal in the second period as Marlon Pack smashed a shot inches wide on 50 minutes before Phillips raced off his line to halt a Mohamed shot.
Moore screwed a shot wide of goal with 10 minutes left at the other end, but had the final say of the final a minute later with the clinching goal.
Crewe last gained promotion to England's second tier in 1997 when they overcame Brentford 1-0 at the old Wembley.