The game finished 1-1 after extra time courtesy of substitute William Abbotts' 90th minute equaliser, cancelling out Otis Khan’s first half opener.
Despite a valiant display from the Bolton youngsters, the Yorkshire outfit came out on top in the penalty shootout, converting all four of their penalties.
The Baby Whites made one change from their 4-1 win over Wolves last weekend, with Robert Holding coming in for Greenhaugh.
The travelling Blades, who knocked out Worcester City in the previous round, were looking to continue their impressive form in the FA Youth Cup in recent years after reaching the final in 2011.
On a cold December evening at the Reebok, the hosts began in emphatic fashion and within two minutes created their first goal scoring opportunity when skipper Sam Bailey forced an early save from United custodian Jake Eastwood.
Five minutes later at the other end of the pitch, William Jaaskelainen, son of former Bolton stalwart Jussi, made an important save with his outstretched left leg to deny winger Dominic Calvert-Lewin from close range.
From there chances became very few and far between for both sides but against the run of play United took the lead with 34 minutes gone on referee Jason Tyas’ clock.
A perfectly weighted through ball from the right wing by Joel Coustrain played Otis Khan in on goal with the striker finishing the job by delicately slotting the ball beyond Jaaskelainen into the far corner.
David Lee and Tony Kelly’s youngsters didn’t let their heads drop after falling behind however and looked for a quick route back into the tie.
In the 40th minute, Bailey, who had the opening chance of the game, tried his luck from the edge of the ‘D’ but the teenager couldn’t connect with the ball properly to worry Eastwood.
With work to do in the second period, Bolton came out with real purpose and energy looking for an equaliser and put in a couple of early testing crosses for the Blades to deal with.
Jaaskelainen was made to work for the first time in the second half with 54 minutes gone, showing superb reactions to get down low to collect a fierce low cross from Jake Eyre.
After an hour, Lee and Kelly made their first change of the evening as Jamie Hinchcliffe came off for William Abbotts, an alteration that later proved to be vital.
United could and should have doubled their lead with 25 minutes remaining when an exquisite chip pass from Connor Dimaio caught the Wanderers backline off guard, leaving Coustrain unmarked in the penalty area, but the winger’s lifted effort clipped the frame of the bar.
The crossbar once again came to Bolton’s aid in soon after as Dimaio hit a powerful strike from the edge of the area, only to come bouncing back and away to safety.
For a third time in quarter of an hour, United were denied by the woodwork and a chance to put the tie out of reach as Khan curled a 20-yard free-kick round the Bolton wall, clipping the outside of the left hand post.
A couple of important saves from Jaaskelainen followed before right at the end of the game, Wanderers found an equaliser to ensure extra time at the Reebok Stadium courtesy of a unstoppable 25-yard strike from substitute Abbotts.
A further 30 minutes now remained as both teams looked to book their place in the fourth round of the FA Youth Cup, with Bradford City or Millwall awaiting in the next stage.
Abbotts, buoyant from his late equaliser, nearly turned the game completely on its head four minutes into the first period, but Eastwood was on hand to beat the ball away.
Both teams continued to work hard for the all-important third goal, however despite a couple of half chances for either team, the tie was left to be decided from the penalty spot.
Bolton: Sam Bailey – Goal
Sheffield United: Connor Diamio – Goal
Bolton: Elliott Newby – Goal
Sheffield United: Dominic Calvert Lewin – Goal
Bolton: Jamie Thomas – Goal
Sheffield United: Otis Khan – Goal
Bolton: Guillermo Torres – Saved
Sheffield United: Jason Paling – Goal
Bolton: Robert Holding – Missed
Sheffield United win 4-3 on penalties
Bolton: Jaaskelainen, Hendrie, Honeyball, Ball, Holding, Bailey, Newby, Cvetko (Kennedy 79), Torres, Hinchcliffe (Abbotts, 61), Thomas.
Sheffield United: Eastwood, Paling, Ptak (Ishmail 89), Whiteman, Evans, Banton, Calvert-Lewin, Dimaio, Eyre (Cockerline 64), Khan, Coustrain, (Reed, 74)