Morrison's sixth goal of the season gives Blues a share of the spoils.BCFC
Enda Stevens fired the Blades into the lead with a brilliant strike. But Blues hit back before half-time through skipper Michael Morrison.
And in truth United had to be thankful to goalkeeper Dean Henderson for keeping them in it after the stopper produced several excellent saves; including an absolute world class one to deny former Blade Che Adams.
Garry Monk made one change to the side that overcame Leeds last weekend, with the injured Maikel Kieftenbeld being replaced in the centre of midfield by David Davis.
United made the brighter start, with Blues guilty of allowing them far too much time on the ball as they sought to create an opening.
Blues were continuing to largely soak up the pressure, before attempting to hit the visitors on the counter.
But it was Blues that almost took the lead in somewhat fortuitous circumstances with just over a quarter of an hour played.
Blues attacked down the right before Connor Mahoney laid the ball off to Gary Gardner on the overlap.
The midfielder drilled a powerful cross into the box, but on the way through it struck Martin Cranie and would have deflected into the top corner of his own net had it not been for Blades 'keeper Dean Henderson scooping it away with a fine save.
Blues had a glorious opportunity to open their account on 30 minutes when Jacques Maghoma's cross found its way to Harlee Dean, but the Blues defender fired over the Sheffield bar from just eight yards.
However, it was the Blades that took the lead with a fine finish with 38 minutes on the clock.
Stevens collected the ball on the edge of the Blues box and drilled it home with a piledriver of shot.
Although Camp got a hand to it, such was the ferocity of it that he was simply unable to keep it out.
Blues' disappointment at conceding didn't last long as they found themselves right back in the game courtesy of captain Morrison less than five minutes later.
A corner on the left was swung in by Mahoney. Gardner's initial header was blocked in front of the United goal line, but it dropped back out to Morrison who stabbed it home from about eight yards.
Half-time: Blues 1 Sheffield United 1
No changes were made by either side at the break.
Blues made a lively start and they had their first attempt of the half with just four minutes gone after Pedersen's swinging cross was met by Jutkiewicz, but his downward header lacked real pace and was comfortably collected by Henderson.
The hosts conceded a free-kick in a dangerous position outside their own box, but Camp did well to keep out McGoldrick’s effort at the far post.
Jota was introduced in place of Mahoney on the hour mark and made an immediate impression.
The Spaniard's great through ball found Adams, who fired off a brilliant first-time effort from the edge of the box, but Henderson was equal to it and tipped it behind for a corner.
Jota then had a more than decent chance himself, but once again it was Henderson to the rescue for United as he saved low down at his near post.
With the game heading into the final quarter, Chris Wilder's side began to pile on the pressure as they went in search of the three points that they needed to return back into the automatic promotion spots.
And Blues were being forced to put their bodies on the line, as they attempted to keep the Yorkshire side at bay.
But sure enough their battling qualities came through to earn them another point towards safety.
Blues (4-4-2): Camp; Colin, Morrison, Dean, Pedersen; Mahoney (Jota, 60), G. Gardner, Davis (C Gardner, 83), Maghoma, Jutkiewicz, Adams.
Subs (not used): Trueman, Roberts, Vassell, Mrabti, Harding.
Bookings: Davis (34), Pedersen (65).
Goals: Morrison (42).
Sheffield United (3-4-1-2): Henderson, Baldock, Stevens, Fleck, Basham, Sharp, Egan, Norwood, McGoldrick, Duffy (Madine, 59), Cranie (Dowell, 59).
Subs (not used): Moore, Hogan, Madine, Coutts, Freeman, Stearman.
Goals: Stevens (38)
Referee: Darren Bond.
Attendance: 23,351 (3,247 away).