But United improved after the break and were only denied victory by the heroics of Forest goalkeeper Lee Camp - making his 200th league appearance.
Camp made a string of fine stops to keep the hosts at bay and ensure Billy Davies' side remain the only league club in England not to have tasted a league defeat on their travels this season.
Davies was not present to witness Camp's impressive performance, however, after being taken ill prior to the match, leaving assistant David Kelly in charge.
With Carl Ikeme sidelined by a calf problem, Sheffield United boss Kevin Blackwell handed a recall to Mark Bunn in goal.
Ched Evans also returned to the Blades line-up in place of Lee Williamson, while Andy Taylor came in for Toni Kallio, who sustained an injury prior to the game.
Forest made just one change following their stunning 5-1 demolition of Leicester at the weekend, with Luke Chambers replacing Radoslaw Majewski.
United's on-loan forward Richard Cresswell saw a snapshot fly wide inside the first minute.
At the other end, Dexter Blackstock headed wide from Chris Cohen's floated free-kick, while Paul McKenna curled a tame shot straight at Bunn from 25 yards.
With clear-cut chances at a premium, Evans tried his luck with an audacious 40-yard lob in the 22nd minute, but Camp gathered with ease.
Remarkably, Evans' ambitious effort proved to be the final attempt on target before the interval.
The dismal standard of play clearly frustrated the vocal home support and their mood was hardly improved shortly before the break when referee Andy Haines waved away appeals for a penalty after Evans appeared to have his shirt pulled in the area.
Goalmouth action remained scarce in the opening stages of the second period as both sides continued to struggle in the final third.
Blades goalkeeper Bunn was finally called into action on the hour mark to tip away a left-footed shot from Robert Earnshaw, although the officials bizarrely awarded a goal kick instead of a corner.
Seconds later, United's Jamie Ward saw a close-range header parried away by Camp before Nick Montgomery's powerful follow-up thundered into the chest of Cresswell, who was duly flagged offside.
Camp made another reaction stop to deny Stephen Quinn in the 68th minute after the midfielder had stretched to get a toe-end on James Harper's lofted through ball.
And Forest's goalkeeper had to be alert to keep out a drilled effort from Blades substitute Henri Camara five minutes later as the game finally sparked into life.
Earnshaw saw a goalbound effort blocked by Chris Morgan before a swift United counter attack ended with Camp making a fine double save with his feet to deny Camara and Quinn.
Camp once again came to Forest's rescue in the 78th minute, keeping out a weak effort from Matt Kilgallon after the centre-half had been played clear through on goal.