The Blades enjoyed the majority of the chances and possession at Bramall Lane - especially when gaps opened after both sides were reduced to 10 men.
The bizarre sendings-off of Sunderland captain Gary Breen and United's Andy Gray threatened to overshadow Shaw's endeavour - but he grabbed the winner after 66 minutes, and his side did not look like dropping the points.
The away side's recent form, which had taken them to fifth in the league, betrayed them tonight against a side who have struggled this season.
Neil Warnock's team have barely got going this season - but will be buoyed by an effort which brought them their first league win after three defeats and a draw.
Although United dominated attacking possession, it was referee Mike Dean who stole the limelight in the first half.
Dean, who sent off three players in the recent clash between West Brom and Fulham, added another two dismissals to his season's tally after 37 minutes.
He sent Breen and Gray off for violent conduct as the Blades took a free-kick, although he and the majority of the 17,908 crowd did not see the incident.
After he consulted his linesman - who was on the other side of the pitch - both were given straight red cards.
The incident did not reflect the game, although the second half then began with a series of fierce tackles. Paul Thirlwell was also booked for a trip on Stephen Elliott just before the hour mark.
The red cards also failed to inspire the visitors who were short of new signing Michael Bridges - and woefully bereft of ideas.
Their main route of attack was the long ball for striker Elliott to chase. He did not get the better of defender Phil Jagielka - although he did have a shot blocked in a dangerous position early in the second half.
Their only shot on target was from Northern Ireland international Jeff Whitley, which Paddy Kenny tipped over easily on 12 minutes.
Whitley spent most of the evening just beyond the back four as the home side pushed forward.
Shaw was their main threat, looking to break when possible and forcing Mart Poom into an acrobatic save midway through the first half.
Recently returned from a loan spell at Rotherham, Shaw looked eager to impress Warnock and cement his place in the starting line-up. Just a minute into the game, Poom saved from his glanced header.
The Estonia stopper was also called into action to save a long-range drive from Jon Harley just before the break - and later to deal with Leigh Bromby's volley which was heading for the top corner.
But Quinn came closest to opening the scoring just after the hour when Michael Tonge found him in space in the area - but again Poom was equal to the effort with a fine, low save from the powerful drive.
Jonathan Forte was brought on after 65 minutes for the ineffective Tommy Black. Despite the huge reception he received, it was Shaw who opened the scoring a minute later.
He pounced on errors from Steve Caldwell and Jeff Whitley and finished low past Poom, with Caldwell prostrate.
Mick McCarthy responded by bringing on Simon Johnson and John Oster for Whitley and Darren Carter - as the Black Cats tried desperately to get something from the game.
With Chris Morgan injured in the first half and taken off after 22 minutes, United played much of the game with tiny full-back Alan Wright at the heart of their defence - but Sunderland could find no way around or over him.
With 10 minutes remaining, the veteran defender instinctively blocked Carl Robinson's header from four yards out.
It was United who looked likely to score again, Forte running from the half-way line and smashing the post with a powerful drive.
It remained 1-0, though, despite George McCartney's late effort which was easily saved.