Goals from Billy Sharp, Hanson, John Fleck and Caolan Lavery gave United victory, which saw them leapfrog Scunthorpe United, who lost at Southend United.
After defeats to Walsall and Fleetwood Town, plus a draw with Gillingham, Blades boss Chris Wilder believes his side's display will silence any critics.
"Individual errors and missed chances over the last three games have not got us the points we wanted," said Wilder, who praised debut-maker Hanson.
"We had a tweak, and the players have been outstanding, a real group effort.
"They have answered a lot of questions out there with their performance.
"The early goal was really important, it's been a good day."
The Blades, looking for their first win in four, gave an immediate debut to former Bradford City striker Hanson.
There was also a recall for Jake Wright, as Marc McNulty and Chris Basham dropped to the bench.
And United took the lead with their first attack inside two minutes. John Fleck's free-ki ck looked easy pickings for the Wimbledon keeper James Shea but he dropped the ball at the feet of Billy Sharp who tapped home from close range.
It was Sharp's 19th goal of the campaign, and coming just 24 hours before his 31st birthday, was most definitely an early gift.
Jake Reeves saw his long-range effort comfortably saved by Blades stopper Simon Moore, in a rare attacking moment from the visitors.
Dave Bassett, a manager who has a long, rich history with both clubs, was watching on from the stands and he will have been impressed with the Blades.
Hanson went close with a far-post header from Kieron Freeman's cross, but the debut striker was not to be denied before half-time.
A super counter attack saw Mark Duffy feed Freeman, who pulled out the goalkeeper, before dragging the ball back for Hanson to fire home on 37 minutes.
United finished the half on top with the threat of more goals to come in the second half for the 20,549 crowd.
Ethan Ebanks-Landell stayed off with a knock at the break, replaced by Basham.
Twice Sharp had chances to put United 3-0 up. First he poked Daniel Lafferty's left-wing cross wide, before latching on to Duffy's pass but failed in his attempt to lob Shea.
Lafferty saw his glancing header go wide, as the Blades poured forward towards the Kop and a third looked inevitable.
It finally arrived on 79 minutes, the impressive Fleck netting in front of the Kop.
Samir Carruthers was introduced late on, for his home debut, but this was an impressive display by the Blades after their recent stutter.
Substitute Caolan Lavery added a fourth goal in stoppage time, stroking the ball into the bottom corner.