Having gone a goal down to Adam Marriott’s opener in first-half stoppage time, the Spireites turned things around after the break and had looked on course for a 2-1 triumph thanks to a Deji Elerewe own goal and Darren Oldaker’s strike.
Michael Cheek dramatically forced extra time, however, with a goal nine minutes into added time, only for Liam Mandeville to grab the winner after 103 minutes, leaving Chesterfield 90 minutes away from ending their four-year exile from the Football League.
The match was delayed by 10 minutes due to crowd congestion, but that did not stop the Spireites making a strong start, with Ryan Colclough forcing Reice Charles-Cook into a low save.
There was a further delay due to an emergency in the crowd, before Bromley took the lead in the eighth minute of first-half injury time.
Ross Fitzsimons was unable to deal with a cross at the near post, allowing Marriott to poke home from a yard out.
Chesterfield upped the ante after the break and levelled when Elerewe turned Colclough’s cross into his own net under pressure from Andrew Dallas.
Bromley, aiming for Football League status for the first time in their history, were reduced to 10 men in the 75th minute when Elerewe was sent off for a tackle on Mandeville.
It did not take long for the hosts to take advantage as Oldaker’s deflected 20-yard free-kick fizzed past Charles-Cook and looked destined to set up their Wembley date.
But Bromley had other ideas and, nine minutes into 10 added on, they sent the game to extra time as Cheek poked home from close range.
The Spireites were not going to be denied, though, and Mandeville sealed their trip to the national stadium by rifling home the winner.
The Welsh team took the spoils in a five-goal thriller between the division's top two sides, capped off by goalkeeper Ben Foster's dramatic 97th-minute penalty save.
It means Phil Parkinson's men move to 103 points for the season, just three ahead of County, and with a game in hand on their rivals after a pair of record-breaking seasons.
Hollywood star Reynolds, who owns the club alongside fellow actor Rob McElhenney, was quick to credit both his team's opponents and Foster's crucial contribution when he spoke afterwards.
"It was a pressure cooker coming into this, I think, for both of these teams," he told BT Sport. "What both have achieved is historic on every level.
"I don't think I've ever seen anything quite like that. When I get my hands on Ben Foster, he's going to be on the injured reserve list, I'm going to break ribs.
"I'm going to hug him so hard. I don't feel like I have a heart anymore. I feel like I used all the beats I have left during that match.
"That was unlike anything I've ever seen before and indicative of all you lifers who have watched and participated in this beautiful, tortuous game forever.
"I'm actually grateful at this moment that I didn't care about this years ago because it would have just eaten me alive. That was really something."
McElhenney, who was also in attendance for the blockbuster encounter, took to social media afterwards, writing on Twitter: "I can’t believe there was a time when I thought football was boring."
Wrexham, who have four games left this season, next face play-off hopefuls Barnet on Saturday.
There has been a great deal of focus on Wrexham over the past two seasons after the club were bought by Hollywood actors Ryan Reynolds and Rob McElhenney.
The Welsh side have thrived in the spotlight, finishing second last year and falling agonisingly short in an epic play-off defeat to Grimsby Town.
Wrexham bounced back this season and are now in pole position for the single automatic promotion place, needing only to beat Boreham Wood on Saturday to seal their return to the Football League.
That is only after a remarkable tussle with Notts County, however, culminating in the dramatic 3-2 Easter Monday win at the Racecourse Ground.
Both Wrexham and Notts have passed 100 points, with the league leaders setting a points record for the top five divisions of English football.
For defender Tozer, that incredible standard encourages comparisons with perhaps football's greatest rivalry, which saw Messi at Barcelona and Ronaldo at Real Madrid hit their peaks at the same time.
"Everyone would rather have won the league by March, and that's just the way things are," Tozer said, looking forward to the Boreham Wood game.
"People generally want things easy, but if you want to go and win a league, it's tough, it's hard. You have to do the right thing day in and day out.
"And again, it's been great to have that pressure. It probably was the same. We'd both be pushing each other really, and that's okay.
"It's a bit like the Messi and Ronaldo situation pushing each other on. It's been tough and it's been good."
