Billy Sharp's hat-trick could only earn the Blades a draw after a dramatic late Villa fight-back.
Villa scored three times in the final ten minutes of a exhilarating contest in the midlands with Sharp taking the plaudits for United.
Loanees Madine and Dowell started as boss Wilder made two changes. The duo replaced McGoldrick and Duffy, who dropped to the bench.
The Blades, undoubtedly, made the brighter start and the first shot on target came from Baldock but goalkeeper Kalinic pushed away. The visitors whipped in crosses from both sides and Dowell looked a threat ahead of the opening goal on 11 minutes.
Norwood's deep corner was headed back into the danger area by Madine and SHARP nipped in ahead of his marker to poke home. Abraham cleared from behind the line and for confirmation Hawkeye's technology gave the referee the confidence to signal the goal.
Villa came back into the game after falling behind but O'Connell produced a covering tackle to stop Abraham, who, moments later, headed wide at the back post from Hourihane's cross.
There was also a Hutton half-volley which flew over the top but United managed to get back on top as half-time approached.
Just after the interval Madine had two half-chances - the first after cutting inside from the left but Kalinic was well placed and then the big striker could not get enough on a low Baldock cross.
But like the first half, United's impressive start to the second period was rewarded. Dowell's shot was pushed away by the home goalkeeper, who then dallied as he tried to keep out Madine's follow-up header, allowing SHARP to prod home from less than a yard. Villa protested but their pleas fell on deaf ears.
McGinn's effort was blocked by Egan before United added a third in less contentious circumstances. Dowell again got around the back of the Villa defence and his right-foot cross was deflected perfectly into the path of SHARP to score again from close range.
Madine received an ovation from the Blades fans as he was replaced by McGoldrick, whilst Cranie also took over from Dowell as Villa attempted to get back into the game - Hourihane's free-kick from the edge of the box was pushed away by Henderson.
On 76 minutes McGoldrick had an opportunity to make it four but Kalinic saved and the remaining minutes saw United put on the back foot. Villa were given a lifeline on 82 minutes as MINGS rose highest to head home a Hourihane corner.
They added a second on 86 minutes as ABRAHAM found himself unmarked at the back post to touch home after Henderson could only parry Elphick's shot. The fans who were leaving the ground did a U-turn and the home side were aided by five minutes of added time.
And the equaliser came in the fifth of those extra minutes as substitute GREEN rose above Baldock to head home at the back post. The final whistle followed shortly after, signalling another point, rather than three, to the tally.
Villa: Kalinic, Taylor, McGinn, Hourihane, Jedinak (Whelan 65), Abraham, Hutton, El Ghazi, Elphick, Kodija (Green 65), Mings.
Unused: Steer, Bjarnason, Elmohamady, Hause, Adomah.
Blades: Henderson, Baldock, Stevens, Fleck, O'Connell, Basham, Dowell (Cranie 74), Sharp (Washington 85), Egan, Madine (McGoldrick 69), Norwood.
Unused: Stearman, Duffy, Johnson, Moore.