Plymouth registered their first win at Bramall Lane for 69 years and in the process ended United's six-match unbeaten run in the Championship.
In an eventful game, the woodwork was struck four times, Ian Bennett made two top-drawer saves and David Carney had an effort ruled out.
However, the decisive goal, midway through the first half, came from Hungarian international Peter Halmosi when he lifted the ball over Bennett after slicing through the Blades defence.
Boss Robson was afforded the luxury of naming an unchanged team for the third successive game, whilst managerless Plymouth replaced the suspended Timar with Doumbe. Just before kick-off the whole ground was united in an appreciative minute's applause for Joe Shaw - the Lane's leading appearance maker - who died earlier this week.
The visiting side did well early on and Martin twice tried his luck in the first seven minutes. His first effort was relatively comfortable for Bennett and Naysmith blocked the second.
On eight minutes Beattie looked favourite to connect with Bardsley's cross but Connolly cleared and then twice United were almost aided by the visitors. Beattie latched onto a back-pass from Nalis but was not in a position to work an opportunity and then a Hodges header almost caught out goalkeeper Larrieu with Webber poised to benefit.
In between these efforts, Plymouth went close to opening the scoring on 14 minutes. Kilgallon misjudged a Connolly clearance which put Ebanks-Blake in the clear but he recovered to make a challenge, helped by defensive partner Cahill.
Halmosi fired over from 25 yards and Webber attempted a long range effort on 20 minutes after seeing Larrieu off his line but the shot was off target.
Plymouth, however, went ahead with their next attack, on 24 minutes. From Ebanks-Blake's ball through the defence, HALMOSI beat the offside trap and lifted over the advancing Bennett into the net, via a post. The travelling fans, a good number coming from the west country, decided to remind Ian Holloway what he was missing.
Montgomery came close to levelling on the half hour, striking the outside of the post following Beattie's lay-off but Plymouth remained dangerous and despite the attentions of Kilgallon and Armstrong, Hayles got in a shot at Bennett.
Armstrong attempted a half-volley, which was just wide following a throw and then Carney had the ball in the net on 41 minutes but the linesman's flag was raised when the Australian got onto Beattie's pass.
Just when United were beginning to get back into the game, Plymouth stepped up a gear and came close to extending the lead before the break. On 44 minutes, Ebanks-Blake got the better of Cahill and in a two-on-one situation, he ignored Martin's pleas for a pass and shot but Bennett tipped the ball over.
From the resulting corner, the last notable action of the half, Halmosi crashed a powerful effort against the angle of post and crossbar and Ebanks-Blake was flagged offside as he looked to get on the end of the rebound.
Halmosi began the second half like he ended the first, with a long-range effort but this time Bennett was ideally positioned to get his body behind the ball, whilst at the other end, Beattie attempted a 30-yard shot which flew over, although Larrieu was again off his line.
Naysmith's timely tackle halted Hayles and Plymouth looked dangerous again and then, with 55 minutes gone, Ebanks-Blake smashed a swerving, powerful effort which surprised a few by cannoning against Bennett's post.
With the crowd getting restless, Robson made changes just before the hour, taking off both wide players but within minutes, United were thankful to Bennett on two separate occasions.
On 62 minutes the goalkeeper spared Montgomery's blushes after the midfielder's pass put Ebanks-Blake in the clear and then Bennett stayed on his feet long enough to make a vital save from Martin after a Ebanks-Blake had put him in the clear.
Bardsley was booked for an alleged dive on the edge of the box - a decision that incensedtyboss Robson - and Larrieu saved from Tonge's left-foot effort.
Webber couldn't believe his luck on 74 minutes when he was twice denied. From Tonge's corner, Beattie won the header and Webber's initial effort was cleared off the line by Halmosi, whilst from the rebound the striker fired against the crossbar.
Beattie headed at Larrieu from Montgomery's cross and Sharp had an effort blocked as United piled on the pressure late on.
Plymouth, unsurprisingly, attempted to slow the game down but four minutes of added time raised the noise levels amongst the Blades fans in the ground. However, without another chance, it was the travelling supporters that were singing at the final whistle.
Blades: Bennett, Naysmith, Bardsley, Beattie, Webber, Carney (Sharp 58), Kilgallon, Montgomery, Gillespie (Tonge 58), Armstrong, Cahill.
Unused: Kenny, Morgan, Stead.
Plymouth: Larrieu, Connolly, Nalis, Norris, Ebanks-Blake (Easter 86), Hayles, Doumbe, Halmosi (Sawyer 77), Hodges, Seip, Martin.
Unused: Fallon, Sawyer, McCormick, Abdou, Easter.



















