The Terriers remain in the top six, the Blades were only outside on goal difference ahead of the 3pm kick-offs.
Huddersfield missed out on a penalty but Pipa perhaps had himself to blame.
The game opened up more in the second half with Huddersfield dangerous on the counter-attack and Oli McBurnie not quite able to make the most of the chances. The teams took it in turns to have spells of dominance each per half.
Frustrated though both will have been not to win, they are taking steps in the right direction. The Terriers are unbeaten in 14, the Blades only six but they feel like they are building up the head of steam they need after giving the rest a head start early season, then seeing their momentum checked by Covid-19.
Both sides passed the ball patiently but found playing through the opposition very difficult.
Huddersfield had a stroke of luck in the 38th minute but it was paid back with interest when Jon Russell's header at a corner a minute later was wrongly disallowed.
With the game taking place on the Saturday lunchtime after both teams had played on Wednesday night, each manager felt the need to make four changes with Carlos Corberan's the more surprising, with first Championship starts for Russell and Josh Ruffles.
On paper, the home side had the more width but with Pipa usually coming inside from right-back, it was acutally the Blades who made better use of it when the game finally opened up a chink after a first 20 minutes or so of stalemate.
Jayden Bogle put a cross in which the recalled McBurnie did well to get to, but Nicholls grabbed onto the ball. He headed another wide when Fleck - another fresh pair of legs - got out wide on the left to deliver the ball for him.
His fellow centre-forward Danny Ward looked the Terriers' best bet but he too did not see enough of the ball. He headed a Pipa cross wide in the 18th minute and shot just wide when he pounced onto a loose square pass.
Although Huddersfield were playing 4-3-3, Jonathan Hogg was regularly dropping in as a third centre-back out of possession to help out with McBurnie and the ever-dangerous Billy Sharp.
Hogg could count himself lucky that the offside flag went up when he brought Sharp down as he ran through on goal.
A minute later giant midfielder won his header at a Sorba Thomas corner but the goal was scratched off because Ward had hurtled into Wes Foderingham as he tried to save. The replay - not available to officials in the Championship - showed left wing-back George Baldock had thrown the striker there.
The second half got off to a lively start, a very Sharp turn and shot just wide inside the first minute and vital interceptions by Hogg to cut out a Morgan Gibbs-White pass to the striker and two by John Egan. McBurnie almost fell onto a pass from Sharp, directing it straight at Nicholls.
Huddersfield began to be the most threatening team, Josh Koroma forcing a save after a move which featured a couple of beautifully-threaded passes. Hogg headed wide at a near-post corner.
Pipa had a penalty appeal turned down late on, referee James Linnington perhaps thrown by the dramatic way he went to ground after a Jack Robinson challenge.
Paul Heckingbottom brought on Oliver Norwood to try and stem the counter-attacks, Corberan introduced Duane Holmes and Danel Sinani for a bit more creativity.
The Blades finished the stronger and Nicholls had to make a crucial save. He had denied Gibbs-White and Sander Berge around the hour mark but his save from Fleck after 85 minutes was another level altogether, turning his steered shot onto the post, then batting the rebound behind.
It would have been harsh on either side to lose, and Huddersfield's outstanding goalkeeper ensured his side did not.
Huddersfield Town: Nicholls; Pipa, Pearson, Lees, Ruffels (Sinani 78); Russell, Hogg, O'Brien; Thomas, Ward (Toffolo 88), Koroma (Holmes 66).
Unused substitutes: Rhodes, Blackman, Turton, Eiting.
Sheffield United: Foderingham; Basham, Egan, Robinson; Bogle, Berge, Fleck, Baldock; Gibbs-White (Norwood 72), McBurnie (Ndiaye 86), Sharp.
Unused substitutes: A Davies, B Davies, Hourihane, Goode, Jebbison.
Referee: J Linington (Isle of Wight).