Goals from Peter Ndlovu in first-half stoppage-time and Dean Windass shortly after the restart looked to have set the Blades on the way to a victory that would have got their automatic promotion challenge back on track after last week's defeat by Millwall.
But Darren Bent gave Ipswich hope when he pulled one back, Darren Ambrose hit a deserved equaliser, and Bent popped up again with a late winner to seal an amazing triumph.
Ipswich had recovered from three down in an epic FA Cup tie at Bramall Lane last month before losing, but this time their never-say-die attitude paid off.
It was all the more creditable as they had lost leading scorer Pablo Counago after 20 minutes when he saw red for violent conduct in an off-the-ball incident which left Blades midfielder Michael Brown holding his head. It was his second red card this season.
The Spanish striker was the second Ipswich player to be dismissed in consecutive matches, with Hermann Hreidarsson getting his marching orders in the defeat by Bradford last week.
United punished the 10 men with a goal from Ndlovu as the first half drew to a close, the winger turning past Thomas Gaardsoe before striking a good finish to reward the Blades for their superiority.
Ipswich sent on former Sheffield United striker Marcus Bent in an attempt to spice up their attack in the second half, but within five minutes they looked down and out.
Veteran striker Dean Windass burst through on a counter-attack to give the visitors a two-goal lead with a shot from the edge of the box.
But Ipswich, with fired-up Marcus Bent causing all sorts of problems, refused to lie down.
Tommy Miller had already lobbed a shot on to the bar when Darren Bent scored his 12th goal of the season, hitting a 12-yard volley from Jermaine Wright's pass after 57 minutes.
With United suddenly looking jittery, Joe Royle's men pressed for the equaliser and when it came, they thoroughly deserved it. Darren Bent swung over a 78th-minute cross from the right and Ambrose headed the ball past Paddy Kenny.
The winner came after 88 minutes when Ambrose returned the compliment, crossing from the left for Darren Bent to get in a far-post header for his 13th of the season.