Che Adams’ first two goals for the Blades delivered a remarkable comeback but their Capital One Cup odyssey is over after late heartbreak at Bramall Lane.
The 18-year-old scored twice in the space of 140 seconds to overturn Tottenham’s lead in the second leg and draw the semi-final tie level.
But Eriksen - whose stunning free kick had Tottenham in front at half time - scored with three minutes remaining to send the Premier League side into a final against Chelsea.
Extra time looked certain after Adams’ quick-fire double, delivering a brilliant comeback through another brave performance from Nigel Clough’s side.
However, Eriksen showed his quality for the second time on the night to see Spurs back on top.
United had started the first half well and it took a clearance off the line from boyhood Blade Kyle Walker to prevent them from levelling the tie up in the early stages of the second leg.
Spurs keeper Michel Vorm dropped Jamal Campbell-Ryce’s searching cross under press from Marc McNulty who then provided the lay-off which Murphy fired on goal, only to see Walker block on the line.
Tottenham showed their teeth early as they looked to put the Blades to bed at Bramall Lane.
Argentinian forward Erik Lamela cut inside from the right and curled an effort just wide from the corner of the box.
And after Murphy’s chance, Tottenham threatened again when Harry Kane was played in by Lamela but produced a tame shot which drew a simple save from Mark Howard.
Moussa Dembele tried his luck from 25 yards but his low drive never troubled Howard.
Kane went for an early shot to try and catch Howard out on 19 minutes but sliced his effort well wide.
Then Spurs went in front with a moment of individual brilliance from Eriksen.
The Danish forward curled a brilliant free kick from 25 yards that rattled into the top corner off the inside of the post with 28 minutes gone.
After going ahead, Spurs managed the game well, keeping possession in midfield for long periods and pressing the Blades high up the pitch.
United had little sight of the final third but went close three minutes from the break when McNulty’s first touch from a Stefan Scougall pass set him up for a volley which he hooked narrowly wide from the edge of the box.
It could have been even worse for United in the opening moments of the second period when Harry Kane found space for a shot ten yards out but pulled his low strike wide.
United enjoyed their best period of the game to that point after 55 minutes, pushing hard into opposition half without ever really having sight of goal.
Kane drilled a powerful free kick on target with 65 minutes gone but it did not trouble Mark Howard.
Ryan Mason was played into the area by Erik Lamela moments later but he put it wide under pressure.
Then the Blades surged into life, spurred on by the introduction of Adams who would quickly take centre stage.
First, Ryan Flynn’s low cross ran through to the youngster 15 yards out and he slammed a strike on the angle past Michel Vorm.
And moments later Adams struck again. After a scramble, the ball dropped for Adams and he fired home via a wicked deflection.
United made an excellent fist of winning the tie out right after Adams’ second.
Fellow substitute Louis Reed went close from the right corner of the box but fired over.
But then came a 87th minute suckerpunch.
Kane slid through a superb pass which Eriksen allowed to roll across his body before hooking the ball into the far corner.
Blades: Howard, Harris, Basham, Flynn, Doyle (Reed 65), Murphy, Scougall, Baxter, McNulty (Higdon 74), McEveley, Campbell-Ryce (Adams 74)
Subs not used: Turner, Alcock, Kennedy, Wallace
Tottenham: Vorm, Walker, Dier, Vertonghen, Davies; Mason (Rose 90), Stambouli; Lamela (Townsend 74), Dembele, Eriksen; Kane
Subs not used: Friedel, Paulinho, Soldado, Adebayor, Fazio.
Ref: Mike Dean (Wirral)
Cards: Yellow: Doyle 45, Flynn 58 (both Blades); Walker 37, Mason 47, Dembele 55 (all Tottenham)
Att: 30,236 (5,486 away)