After a goalless first leg and a similarly even first 85 minutes at Bramall Lane, extra-time looked on the cards until Porter popped up at the back post to nod Matt Lowton's pinpoint cross past Chris Day.
It sent the home fans wild and was a moment of personal glory for Porter, who had struggled in a lone role up front.
The win was nothing less than United deserved, though, as they were the dominant force throughout and it should have been a more resounding victory, but Ryan Flynn, Lee Williamson and Stephen Quinn were all denied.
As it was, Porter's goal was enough to secure passage to Wembley where Danny Wilson's side will meet either Huddersfield or MK Dons, who play the second leg of their semi-final on Tuesday night.
There was a sense of missed opportunity for Stevenage, who finished 17 points below their hosts in the league, after the stalemate in Friday's first leg and boss Gary Smith responded by selecting Robin Shroot in place of Craig Reid, while the Blades were unchanged and looking for vengeance for the league fixture between these two sides a fortnight ago.
Wilson's side were held to a 2-2 draw, battling back from two goals down, with the result effectively costing them an automatic promotion place.
United delivered a bright start and they should have taken the lead inside the opening 10 minutes but Porter's header from Williamson's deflected pass was superbly saved by Day, with Flynn volleying the resulting corner over.
The hosts continued to control possession, but they struggled to get into any more threatening positions, with the final ball letting them down far too often.
It was easy to forget that United are the top goalscorers in the Football League as Williamson's effort from distance was their only other shot after Flynn's attempt.
Wilson's half-time team-talk will still have been ringing in United's ears by the time they created their first meaningful effort of the second period, but Flynn could not get enough purchase on his shot from 16 yards out following a poor clearance and it was blocked.
It was much more vibrant from the Blades after the restart, though, and Williamson went close when he turned Porter's cross just wide as they stepped it up, with Flynn missing by inches with a 20-yard drive moments later.
The game began to open up and Blades goalkeeper Steve Simonsen, who had been a virtual spectator throughout, was tested for the first time when he got down to save Luke Freeman's low shot.
Quinn and Williamson both fired over from distance as United's surge began to run out of steam.
Stevenage had hardly presented an attacking threat, but they could have taken an undeserved lead had it not been a fine finger-tip save from Simonsen, who superbly turned Scott Laird's 20-yard shot over.
As the game entered its final 10 minutes it became frantic as the hosts renewed their searched for a winner and Matt Hill rifled a 30-yard piledriver just wide and Quinn forced Day into a save with a right-footed effort soon after.
And with extra-time looming, Porter rose highest to nod home from close range and send United to Wembley as they saw out a nerve-wracking final few minutes.