His team were 14th before this game and Beattie's 10th and 11th goals of the season helped secure their first home league win since September 15, their third in eight home games so far.
Jon Walters' lob cancelled out Beattie's clinical 33rd-minute effort but the blades responded and the club-record signing Beattie added a second from the penalty spot before Gillespie smashed in a third late on to give United fans some of the entertainment they have sorely missed in recent weeks.
Ipswich were the team playing the better football in the early stages and Alan Lee almost connected with a low Walters cross from the right.
Lee had another good chance after 20 minutes when David Wright's pass found him in space on the edge of the box, but his scuffed effort drifted just past the post.
United's first decent effort came when Phil Bardsley flashed a low shot wide after being teed up from the set-piece resulting from a clash of heads between Beattie and Wright.
There was a spring in United's step at last after a sluggish start and they scored after 32 minutes when Chris Armstrong calmly squared the ball to Beattie in the box and the former Everton man applied the equally cool finish.
He should have added a second late in the half but headed over Danny Webber's cross from the left.
Ian Bennett comfortably saved Lee's downward header from a Wright ball in at the other end and the Blades were inches away from a second on the stroke of half-time when Webber's curling shot came back off Neil Alexander's left-hand upright.
Ipswich equalised out of the blue nine minutes into the second half when a long ball over the top caught out the Blades and Walters raced on to lob the ball over Bennett.
The former Chester man then headed against the bar from Lee's cross from the left before the danger was cleared with Bardsley having earlier drilled a shot wide for the hosts after Ipswich failed to clear a hanging ball in from David Carney.
United had a strong claim for a penalty when Gillespie appeared to be fouled by Dan Harding in the box, but bizarrely a free-kick was awarded just outside by referee Graham Laws, to the disgust of the home fans.
The next call went their way as Nick Montgomery was judged to have been fouled in the area by Harding and Beattie confidently tucked the penalty away with 20 minutes to go.
It was all hands on deck at the back briefly for the hosts but any fears of an Ipswich equaliser disappeared when Gillespie gained possession after an Armstrong shot was blocked, cut in from the left and cracked a right-foot shot beyond the helpless Alexander.