The tricky Irish winger, signed from Middlesbrough in January, opened the scoring in the first half before laying on goals for Ched Evans and Richard Cresswell after the break to give the Blades their first away win in the league since December 5 to finish eighth.
United's record signing Evans had gone 25 games without a goal, with his last strike coming way back in October, while Cresswell finished the campaign with four goals in his last five matches.
Defeat for Ipswich, who finished 15th, was only their fourth at Portman Road in the Championship this season and Roy Keane's side had 18-year-old defender Tom Eastman sent off on his debut in the second half on what proved to be a miserable final afternoon of the season.
Yeates had a strike at goal in the second minute but fired over the crossbar from long range.
Keane's side responded and Grant Leadbitter tried his luck from 25 yards but Paddy Kenny made a comfortable save.
The home side were again denied by the woodwork after 26 minutes when Jon Walters picked out Owen Garvan and the midfielder's header struck the post.
The Blades made the most of that stroke of luck as they took the lead 12 minutes before half-time.
Gary Naysmith picked out Yeates and the former Boro midfielder slotted home with a clinical right-footed shot from the edge of the penalty area.
Jack Colback had a chance to equalise three minutes later but the on-loan Sunderland midfielder fired over the bar from 12 yards out.
And highly-rated young striker Connor Wickham also failed to hit the target with a header just before the break as the Tractor Boys pressed for an equaliser.
United made a bright start to the second half and Yeates swung over a corner which 19-year-old debutant Matthew Lowton headed wide.
But Kevin Blackwell's side doubled their lead 10 minutes into the second half when the impressive Yeates crossed from the right and Evans slotted home with his left foot.
The afternoon went from bad to worse for the hosts two minutes later when 18-year-old defender Eastman was shown a second yellow card for a foul on Lowton.
Yeates was at the heart of most of United's attacks and he forced Brian Murphy to make a good save 61 minutes in.
But the Blades made their numerical advantage count when Yeates once again provided the assist, this time for the in-form Cresswell to head home from six yards out.
Troy Brown was denied by Kenny as Ipswich pressed for a consolation without success.