Jamie Proctor's second goal of the season ensured Reds stretched their unbeaten run in League One to six after a hard-fought draw at Bramall Lane.
Proctor gave Reds an early lead with a close-range header and before the break Crawley had good chances to stretch their lead. United rallied in the second half and levelled through Marlon King and in the closing stages an entertaining game could have gone either way.
Reds' boss Richie Barker made one change to the side that beat Oldham last Saturday with Proctor starting up front in place of Emile Sinclair, who dropped to the bench. Gary Alexander returned after a suspension as a substitute while Kyle McFadzean was named captain against his former club.
Reds made a bright start and forced a corner in the third minute. McFadzean drove into the box down the left but his low cross was gathered at the second attempt by home keeper George Long.
The Blades then won a free kick 25 yards out on five minutes which ex-Reds' midfielder Ryan Hall curled over the wall but straight at Paul Jones but on nine minutes Reds went in front. Andy Drury played a short corner to Billy Clarke and when he got the return Drury chipped the ball to the far post where PROCTOR had a free header for his second goal of the season.
Mat Sadler and McMahon were booked after a touchline tussle and the United defender broke into the box on 17 minutes but his deflected shot was pounced on by Jones in the six-yard box.
Reds nearly went further in front midway through the half. Sadler burst into the box and Billy Clarke and Proctor were waiting for a tap-in but the pass was over-hit and United were eventually able to clear.
The visitors were in control at this stage as the home fans started to vent their frustrations, although they were nearly cheered up 11 minutes before the break when a corner was met by Harry Maguire but he guided his header well wide of the right-hand post. Reds broke moments later, but Clarke's cross after he burst into the box was cut out as Nicky Adams waited to pounce.
Just before the break the visitors had two more good chances. Joe Walsh won the ball off Marlon King and broke forward before rolling a pass out to Proctor, but his angled drive went wide of the near post. Moments later Clarke set up Adams for a run at the home defence but his shot also failed to trouble Long. At the other end Febian Brandy's shot in stoppage time which was straight at Jones drew ironic cheers from the home fans.
As expected, the home side stirred themselves at the start of the second half and on 52 minutes were nearly level when McMahon's right-foot drive from 25 yards beat Jones but came back off the inside of the post.
It was a let-off for Reds but they responded well and Adams' appeals for a penalty after he went spinning in the box fell on deaf ears. Moments later McFadzean was booked for a foul on Brandy.
But there was more urgency about the home side and they drew level on 63 minutes. Brandy's clever pass gave KING an opportunity and he clipped the ball over Jones to score his first goal since his move to Yorkshire last month.
Reds made their first change midway through the second half when Proctor was replaced by Gary Alexander and with 11 minutes to go James Hurst came on for Drury.
Alexander was inches away from connecting with Adams' inviting cross in the last ten minutes while at the other end King teed up Connor Coady whose side-footer was pushed around the post by Jones.
But Reds were still a threat as they continued to attack intelligently and moments from the end of normal time Long was forced to make a scrambling save from a shot by Sergio Torres, who had just replaced Adams.
Blades pushed in stoppage time and Jones had to save a shot from substitute Jamie Murphy for a corner which Reds cleared.