Rumours about the midfielder's future have surfaced again this week - Rangers are the latest club to be linked with a move - but Brown's value to the Blades cause was underlined during a lively first half in which he opened the scoring from the penalty spot.
He also played a part in United's second goal, setting up Stuart McCall to seal victory 15 minutes from time.
With discussions over a new contract, which runs out at the end of the season, underway, Brown could not have chosen a better time to underline his talents.
If Brown was the central figure of an entertaining encounter at Bramall Lane, Preston's failure to convert any of a host of chances was also a major talking point.
They spent much of the second period camped inside the United half, but a combination of wasteful finishing, resolute defending and superb goalkeeping from Paul Gerrard ensured they left Yorkshire without a win in three games.
The visitors were the first to threaten, and it needed a superbly-timed tackle from Rob Kozluk to deny the rampaging Ricardo Fuller.
Wayne Allison failed to test Jonathan Gould with a mistimed volley - he had another effort blocked by Marlon Broomes - but Preston's pace on the break continued to trouble the United back-line.
Fuller shot wide, Eddie Lewis forced a smart save from Gerrard and Richard Cresswell's strike was tipped over in the space of three minutes.
Brown struck the wall with a 25-yard free-kick, and stung Gould's palms before he broke the deadlock in the 31st minute.
Jack Lester fell under the goalkeeper's challenge as he broke into the Preston penalty area, and Brown found the bottom left-hand corner of Gould's net with the spot-kick.
The opening seconds of the second half saw Paul Gerrard and Gould pull off superb saves to keep out long-range efforts from Graham Alexander and Michael Tonge respectively.
Peter Ndlovu, a 48th-minute replacement for Mark Rankine, produced an early cross which Allison narrowly failed to convert, but Preston served further notice of their threat on the break when Fuller's drive was brilliantly kept out by Gerrard, playing his last game before his loan spell from Everton expires.
Though Brown sent a curler narrowly the wrong side of the post from just outside the area, it was a rare moment of relief for the hosts as Preston's pressure continued to mount.
David Healy, brought on in place of Dickson Etuhu, missed the chance to cap a flowing North End move when he nodded wide, Fuller's drive struck Phil Jagielka and Brian O'Neil also misdirected a header.
Preston were punished for the profligacy almost immediately, McCall shooting through Gould's legs after latching on to Brown's flick-on.