Goals from Ollie Norwood and David McGoldrick saw United add another three points to their tally, but that didn't tell the whole story of an eventual night at the Lane.
After Norwood had fired home a first-half penalty, Gary Madine was given a straight red card, leaving United with 55 minutes to play with ten-men, but heroic and David McGoldrick's goal ensured the Blades kept the pressure on the top two in the Sky Bet Championship.
For the midweek encounter, boss Wilder made two changes, with Dowell and Madine starting in place of Duffy and McGoldrick, who dropped to the bench.
It was a quiet opening ten minutes at both ends. Daniels claimed a Fleck cross with Hogan inches away from contacting, whilst at the other end, Watkins fired into the Kop after some neat build-up play. United's first corner of the night fashioned a chance, but Madine couldn't direct his header on target.
On 14 minutes, the deadlock came closer to being broken. Dowell evaded two challenges before playing the ball to Fleck, he unleashed a powerful effort, but with Daniels beaten it went just too high. But the Blades were then indebted to Henderson, who denied Maupay with a terrific reflex save from Barbet's left-wing cross.
Basham was booked for a foul on Benrahma and from the resulting free-kick, Henderson was again called into action to deny the Bees midfielder. But in the 26th minute, it was the Blades who went in front. Barbet failed to get the ball under control as he looked to come out of defence and after Baldock nipped in front, the assistant referee deemed the defender had committed a foul. From the spot, skipper NORWOOD assumed responsibility and sent Daniels the wrong way.
Ten minutes before the break though, Madine was given a straight red card for a foul Konsa, with referee Harrington quick to make his decision. Moments later the visitors should have levelled, but Maupay fired over on the rebound after Watkins had been denied by Henderson. The visitors continued to press forward, with the ever dangerous Benrahma sending another free-kick inches away from the target.
United made a double change at the break, with McGoldrick and Cranie replacing Hogan and Dowell, a change that saw Basham move into midfield. Within a minute, McGoldrick had registered a shot at goal, forcing Daniels to concede a corner, from which O'Connell saw his header at the back post saved.
Brentford responded and Henderson was at full stretch to deny Maupay. The Bees came even close in the 57th minute as Mokotjo rattled the woodwork from a short corner, on the follow up Jeanvier fired over the top. On the hour, Sharp replaced Baldock, prompting another change of formation.
United went forward, won a free-kick and almost went two goals in front, but Daniels denied Egan from Sharp's pull back. United fashioned another opportunity on the break, but McGoldrick opted to square the ball instead of shoot and his ball was behind Sharp.
The clocking was ticking down in United's favour as they continued to defend resolutely, with Watkins the latest Bee to try his luck, firing high and wide, before Fleck and O'Connell put their bodies on the line to make crucial blocks.
And those were rewarded at the other end with six minutes remaining. Sharp forced Jeanvier into a mistake and from the resulting corner, O'Connell headed back into the six-yard box for MCGOLDRICK to nod past Daniels, to the delight of the majority of the Bramall Lane crowd.
Four minutes of added time were signalled and like they had all evening, United remain solid and saw it out, although Henderson was required to prevent an own-goal, with Norwood under pressure, but it mattered not, as United registered an eighth straight home win, this time against the odds.
Blades: Henderson, Baldock (Baldock 60), Stevens, Fleck, O'Connell, Basham, Dowell (Cranie 45), Hogan (McGoldrick 45), Egan, Madine, Norwood.
Unused: Coutts, Stearman, Duffy, Moore.
Brentford: Daniels, Odubajo (Emiliano 62), Maupey, Watkins, Mokotjo, Sawyers, Benrahma, Dalsgaard (Forss 90),, Jeanvier, Konsa (Canos 62), Barbet.
Unused: McEachran, Gunnarsson, Dasilva, Forss, Sorensen.