In an action-packed game in front of a crowd of 18,790, United maintain the unbeaten start and in the process inflict Bournemouth's first defeat of the campaign.
Ryan Flynn netted twice in the first half, whilst John Cofie scored an impressive goal for a second consecutive week.
After the break Richard Cresswell, in his first appearance of the season, scored three minutes after coming on, before Nick Blackman netted the last of the eight goals with an injury-time penalty.
Flynn replaced Quinn in the only change to United's starting line-up, whilst Cresswell and Westlake were named on the bench - new boy Kitson's signature was not secured in time to play against the Cherries. Before kick-off, the mother and sister of Jessica Ennis were given a rousing reception as they viewed the new stand named in the honour of the Olympic golden girl, who is also a Blade.
The midfield - now including Flynn - again were fluid in their movement early on but the only chance of note came from Cofie, who improvised with his back to goal. Bournemouth's first chance came from a series of mistakes but Grabban's header from a Francis cross was wide.
Left-back Hill was prominent in a lot of United's early attacking intent and was involved in helping win a corner, from which Collins volleyed over on 12 minutes. Grabban then again went close for the visitors, shooting across goal after another attack from the right flank.
A lull gave Bournemouth the initiative and they used it to grab the lead on 20 minutes. A Barnard shot from a corner was blocked but from O'Kane's second delivery, ELPHICK found space to head past the exposed Howard. It took the Blades, though, just four minutes to get back on terms.
McDonald struck the post with a long-range effort in the build up before Hill's deep cross was headed back into the danger area by McAllister for FLYNN to get in front of his marker to slot home on the volley.
Within 10 minutes United - and Flynn - had doubled the goal tally. This time the cross came from the right, McMahon's delivery was met by Addison but the ball dropped nicely for FLYNN to curl perfectly into the corner of the net, beyond goalkeeper Jalal's reach.
The wind was back in United's sails and with Blackman's energy causing problems for Bournemouth's defence, a third goal was not far away. McDonald and COFIE robbed a visitor on the halfway line and the latter strode away before unleashing a 20-yard shot, which may have been deflected slightly but flew into the top corner, over Jalal.
Before the break, when United were warmly applauded off, there was time for another chance - Collins exchanged passes with McDonald but on this occasion Cofie curled an effort against the crossbar.
Bournemouth made a change at the break and did not take long to reduce the arrears. Doyle conceded a corner and from O'Kane's delivery, Howard looked like he was being held back and BARNARD took advantage to head home.
Maguire was being held as he headed Flynn's free-kick into the arms of Jalal but no penalty was forthcoming and soon after there was an ovation as Cresswell was introduced for his first action of the season...that ovation turned into a standing ovation within minutes.
On the hour Flynn found space on the left and his deep cross saw CRESSWELL climb higher than his marker and directly the ball perfectly into the top corner before heading off to celebrate with the Kop.
A good move involving Hill, Flynn and Blackman resulted in McAllister's shot being saved by Jalal, whilst a McDonald shot was blocked over as the United fans enjoyed the second half performance in the sun.
In the final ten minutes, Grabban missed a great chance after Doyle was robbed, but there was a late scare when PUGH was afforded space on the edge of the box, firing into the bottom corner from 25 yards.
There was another scare when Barnard got the better of Hill and Maguire but McMahon cleared to safety over his own crossbar but the Blades survived the four minutes of added time - and even added to the scoreline. BLACKMAN's heels were clipped by Daniels and the striker took responsibility for the penalty, beating the goalkeeper with ease.
Blades: Howard, Maguire, Hill, Flynn, Doyle, Blackman, McDonald, Collins, McAllister, Cofie (Cresswell 57), McMahon.
Unused: Westlake, Miller, Harriott, Ironside, Long, Williams.
Bournemouth: Jalal, Francis, Partington (McQuoid 57), Pugh, Daniels, Elphick, MacDonald (Hughes 45), Grabban, Addison, Barnard, O'Kane (Fogden 77).
Unused: Zubar, Thomas, Tubbs, Flahavan.