© PA Photos
Trailing 1-0 from last week's opening leg at Bramall Lane, hosts Yeovil began the encounter brightly and were able to level up the tie when Kevin Dawson converted James Hayter's through-ball from close range with just six minutes on the clock.
United's response was positive and they went close to going in front in the tie with 32 minutes played, but Jamie Murphy's curling effort from the edge of the area cannoned to safety off the crossbar.
The home side were the dominant force after the restart and should have scored a second when leading goalscorer Paddy Madden rose highest to head goalwards from six yard out, only to see the ball fly wide of the target.
The winning goal eventually arrived in the 85th minute as Madden turned creator for Upson, who guided his header into the corner of George Long's net from eight yards out.
United controlled the possession thereafter, but they were unable to find a goal that would have forced extra time as Yeovil held out for a 2-1 aggregate victory.
They will now take on either Brentford or Swindon Town at Wembley for a place in the Championship next season.