The Red Devils were conductors of the contest throughout in terms of possession but had to wait until late in the first half to take control of the scoreline courtesy of leading marksman Danilo Orsi.
There looked to be a clear way back into the match for Crewe when they were awarded a penalty in the second period, however a VAR-assisted review of the on-field decision concluded that Chris Long had fallen with no contact in the box.
Heading into the final stages of the game, Crawley avoided a nerve-wracking end in the capital by bagging their second of the match via midfield maestro Liam Kelly.
After being tipped for relegation to the National League at the start of this campaign, the Red Devils will now compete in League One for the first time since 2015.
Following the 5-1 thrashing of a lacklustre MK Dons side the second leg of their semi-final clash, Crawley were forced to make one alteration to their impressive XI due to injury, with wing-back Harry Forster dropping out of the squad because of a hamstring strain, being replaced by Kellan Gordon from the start.
Crewe had no such fitness woes ahead of a mammoth date with the Red Devils at Wembley for a place in the third tier, with the Railwaymen naming an unchanged team from the one which completed a marvellous turnaround at Doncaster Rovers last week, with Elliott Nevitt leading the line once again.
Crawley dominate the early exchanges
Having smashed their way through the semi-final stage of the playoffs, final favourites Crawley assumed control of the contest in terms of possession during the opening exchanges, with Lee Bell's Crewe showcasing that they are not afraid to go direct in order to relive pressure.
The Railwaymen were seven games unbeaten (6W 1D) against Crawley ahead of this capital showdown for promotion, however it was the Red Devils who looked more likely to hit the front in the opening 30 minutes, although Liam Kelly's off-target volley was the closest either side got to early supremacy.
Seemingly frustrated with a lack of service, Crewe talisman Nevitt took matters into his own hands on the 37th minute and picked up the ball on the flanks, barged infield and unleashed a low-driven strike from outside the box, however Crawley goalkeeper Corey Addai was able to get down to quickly to parry the effort away.
Impressing with their attractive football in the shadows of England's fourth tier, Scott Lindsey's men put on a show on the biggest stage to take the lead just before the half-time whistle, with Kelly and Orsi exchanging passes prior to the latter turning to earn a yard of space in the box and producing an outside-of-the-foot finish past Max Stryjek.
Having failed to reach his potential so far and missing a fair share of chances last season, Crawley's hitman Orsi bagged his 25th goal of the 2023-24 campaign under the famous Wembley arch, providing a moment of quality in a first half which was a cagey affair.
Crewe nearly provided a lifeline
Following the half-time break, the momentum continued to flow towards the Crewe goal but Crawley were given a mighty scare when midfielder Adam Campbell's poor pass allowed Alexandra attacker Long a clear run through on goal.
The 29-year-old opted to go around Crawley's Addai and was awarded a penalty by referee Ben Toner who judged the keeper to have clipped Long, however a VAR review into the incident revealed that there was no contact between the two parties, leading the decision to be reversed.
With things going remarkably to plan against a side who finished above them in the regular season, there was a hint of complacency from Crawley, however the Red Devils made sure their first-ever Wembley appearance would end in tears of joy as they doubled their advantage in the final 10 minutes.
Making a marauding run through from centre-back, Dion Conroy evaded the attentions of the first line of Crewe's defence and played an incisive pass through to Kelly, whose attempt to find Orsi in the box rebounded back to the Irishman, before he smartly picked out the near post.
Crawley have become the first team since Coventry City's class of 2017-18 to gain promotion during their first-ever playoff campaign, and will welcome the likes of Birmingham City, Bolton Wanderers and Huddersfield Town to Broadfield Stadium next season.