A goal in stoppage time earned the Blades a share of the spoils in London.
United trailed 2-1 midway through the second-half, despite having taken the lead through young debutant Tyler Smith, but Kler Heh produced an excellent finish to net the Blades a point against odds in the opening minute of added time.
After a promising start, Eastwood had to produce two fine saves in quick succession, before United took the lead through 15-year-old Smith, who capitilised on a goalkeeping error before coolly beating the last defender and slotting the ball into the empty net.
United's lead lasted barely five minutes, though. The Blades failed to win a header in midfield and the Lions broke with pace before slotting in the onrushing forward, who equalised.
The second-half saw Millwall dominant for long spells, so it was no surprise when they went in front in the 65th minute, the home striker getting between Brown and Kedman before calmly beating Eastwood.
United, Eastwood in particular, had to produce several timely interventions to keep the visitors in the game and the Blades got their rewards in stoppage time.
Smith was again instrumental to it, his deflected shot fell into the path of Heh in the box and he showed excellent composure to wrong foot two defenders before bending the ball into the far corner.
Coach Travis Binnion was delighted with the character his youngsters displayed in the capital.
He commented: "The game was a really tough one, we were young and inexperienced and at times that showed in our decision making.
"Young Danny Ramsey and Tyler Smith were terrific, whilst Daniel Cockerline led the line admirably.
"Jake Eastwood was commanding and Kler (Heh) showed his ability to net a fantastic equaliser.
"Millwall should have won, without doubt, but we kept going to the final whistle and I am delighted with a point."
Blades: Eastwood, Ramsey, Kedman, Cheeseman, Brown, Ishmail, Heh, Smith, Coustrain, Cockerline, Wright (Slew 68).