Alfie Doughty had put the visitors ahead in the first half, before the Blades hit back during the second period to lead 2-1, Oli McBurnie and Anel Ahmedhodzic on target.
However, Jack Robinson and Anis Slimane then turned two Carlton Morris crosses into their own net as Town triumphed 3-2 and to find out how the Hatters rated on the afternoon, see below.
1. Thomas Kaminski: 7.5
Made one flying save in what was a relatively quiet first half, moving quickly to his left to beat away Hamer’s free kick. With the Blades coming on strong towards the end of the opening 45, hitting the bar, it was a far busier second period, beaten twice by two scruffy goals. Well protected by his defence who threw themselves in the way of some United shots, he managed to shovel Osula’s acrobatic volley over the top in stoppage time and came out well to claim some late crosses into the box. Photo: Michael Regan
2. Ryan Giles: 7
First start since September with Kabore absent, as he slotted into the left wingback role. Positioning was spot on when covering around excellently after it looked like the Blades had got through to face Kaminski. Nipped in to win the ball well at times, making a number of key clearances too. Managed to get forward now at times, but couldn't always pick out a team-mate, sending one dangerous opportunity over the top too. Photo: ADRIAN DENNIS
3. Teden Mengi: 8.5
Since being called on, the centre half has become a real rock on which Edwards can rely on in Luton’s defence. Topped the clearances list at Bramall Lane while also managed to make a terrific block as well. One nervy moment when he sliced Baldock’s cross narrowly over his own bar, but made a wonderful stretching interception when it looked like a volley would fall at the feet of a Blades attacker and thumped the loose ball away too. Photo: Michael Regan
4. Gabe Osho: 8
Like the rest of his defence, bar a few minutes in which Town weren't able to clear their lines, he put in another real shift to ensure Luton left with three Boxing Day points under their belts. Kept possession well in the first half, and an important factor in Luton's comeback as his presence in the area led to Robinson flicking the ball into his own net to make it 2-2. During the closing stages he was able to bring the ball away impressively to relieve some of the pressure on the back-line too. Photo: George Wood