The Blades will take a narrow one-goal advantage to Huish Park in the return leg on Monday after teenage substitute McFadzean's deflected 46th-minute shot settled a tense and evenly balanced first leg at Bramall Lane.
McFadzean, 19, a first-half replacement for injured midfielder Barry Robson, was making only his 11th first-team appearance in his breakthrough season for the Blades and will not have scored a more important goal.
The home side had not scored in their previous three matches and had won only one of their last 10 games to stagger into their second successive League One play-off against Gary Johnson's unsung Yeovil, who had won four of their previous six league games.
The Glovers' confidence, boosted by a 2-0 win at this ground in January, will not have been unduly dented by McFadzean's winner.
The Somerset outfit caused the Blades' defence enough problems - Sam Foley forced home goalkeeper George Long into a fine late save with an overhead kick - to leave them eagerly awaiting the second leg.
Robson curled an early left-footed free-kick inches wide for the Blades and saw his corner headed the wrong side of the opposite post by Porter soon after as the home side made the more purposeful start.
Porter teed-up Jamie Murphy in the 24th minute following another free-kick from Robson, but the Scottish winger blazed his left-footed effort over the crossbar.
The home side were dealt a blow after half an hour when Robson limped off, with McFadzean replacing the former Scotland international.
Yeovil carved out their best first-half opening when Kevin Dawson drove James Hayter's lay-off wide from inside the penalty area in the 36th minute.
But the Blades threatened again from another set-piece when Dave Kitson flashed a header from Darryl Westlake's free-kick just wide.
The Blades, more through endeavour than enterprise, deserved to edge their noses in front following their first attack at the start of the second half.
Murphy crossed from the left having chased Neill Collins' long pass and McFadzean's low left-footed shot from 12 yards deflected off McAllister to wrong-foot Yeovil goalkeeper Marek Stech in the 46th minute.
Yeovil threatened to hit back immediately though, with the assistant's flag denying them an equaliser when Hayter clipped home a neat finish after being set up by Paddy Madden, only to be ruled offside.
The visitors enjoyed their best spell, but the Blades' scrambling defence denied them a clear shot on goal before McFadzean's sublime skill on the right edge of the Yeovil penalty area enabled him to get his shot off and force Stech to save.
Murphy then cut inside to fire a rising right-footed shot wide, but at the other end Collins headed the ball clear after Madden's header bounced goalwards.
Foley's acrobatics then forced Blades keeper Long into a smart reaction save as the visitors pressed for an equaliser, but the Blades held out to leave the tie delicately poised.