While Neil Warnock's men enjoyed possession and the majority of chances, it was the visitors who had clearer sights of goal, producing the kind of performance needed if they are to extend their stay in the Coca-Cola Championship to three years.
Alan Quinn, Danny Webber and Garry Flitcroft all went close for the hosts, but it was Gareth Taylor who spurned the most promising opportunity of the match when he got behind the Blades defence just before the break.
With one win in United's last six outings, the draw gives hope to third-placed Watford, who are only eight points away from the automatic promotion place United have held for much of the season.
Despite their inconsistent recent form, the hosts looked in control initially, with Quinn's volley curling wide in the opening minute after Keith Gillespie's cross was not cleared.
Quinn, one of the radical changes Warnock made to his starting line-up, showed early composure on the slippery surface and found Phil Jagielka on the edge of the area, who drilled a right-footed shot just wide.
Webber, another player restored to the starting XI, was a lively presence in the opening half, forcing Ross Turnbull into two smart saves, the first after taking advantage of indecision in the Crewe area.
The former Manchester United trainee also drilled wide after 24 minutes and saw an effort repelled later in the opening half after turning sharply inside the penalty area.
Quinn had another opportunity 11 minutes from the break but shot straight at Turnbull after twisting to find room on the edge of the area, but for all the Blades' possession it was the visitors who had the clearest sight of goal in the first half.
Madjid Bougherra, the impressive Algerian centre-back, punted a ball beyond the United defence and Taylor shot into the side netting with just Paddy Kenny to beat.
The chance sparked jeers from the home fans - which Warnock warned could be counter-productive in his programme notes - but the Blades boss attempted to lift spirits by bringing Paul Ifill off the bench after 50 minutes to replace the injured Quinn.
The move did little initially, with Crewe midfielder Steve Jones getting a sight on goal before lifting his shot over the crossbar from outside the area.
But the Blades then put the pressure on their lowly opponents, with Chris Armstrong driving into the area and getting his effort deflected wide. From the resulting set-piece Chris Morgan's volley was deflected over.
Flitcroft completed the trio of chances within a minute by lashing wide after Turnbull had shown bravery to smother Webber's close-range effort after Gillespie's corner had caused chaos.
Ifill forced Turnbull into a save after 62 minutes following an exciting run on the left, while Leigh Bromby was taken off shortly after for Nick Montgomery.
Steve Kabba was brought on for Gillespie with 20 minutes left as Warnock looked to chase the game, but it was Crewe who had the next chance.
Luke Rodgers found room six yards out after 72 minutes but smashed his effort into the side netting.
Ade Akinbiyi had a late chance but he shot over the bar, and the striker also had a penalty claim waved away before having a header cleared off the line.
Turnbull also smothered the ball as Akinbiyi challenged in injury time.