Plymouth staged a late fightback in a nail-biting finale after Neil Warnock's promotion-chasing side had struck twice in a seven-minute spell.
Leigh Bromby and Andy Gray broke the deadlock before David Friio hit back for Bobby Williamson's battling side three minutes from time.
Plymouth, who beat United's South Yorkshire neighbours Rotherham four days earlier, forced the early pace. Midfielder David Friio curled a 20-yard free-kick over the top before Phil Jagielka nipped in to cut out David Norris' teasing corner.
United carved out an opening in the 19th minute after Paul Thirlwell picked out Andy Liddell on the right flank. The ex-Wigan midfielder pumped a low cross towards the incoming Danny Cadamarteri who failed to connect eight yards out and Mathias Doumbe cleared.
Cadamarteri tested Romain Larrieu with a close-range header minutes later before Andy Gray, back after a three-match suspension, squandered a chance when he stretched to meet Paul Shaw's flick-on but finished with a tame header that was collected easily by the Plymouth keeper.
The Pilgrims were pushed further back as the Blades looked for the opener, Cadamarteri almost grabbing it as he rose to meet Jon Harley's teasing cross but pulled his header wide of the far post from six yards.
Plymouth escaped in the 62nd minute when David Worrell moved in to cut out Liddell's cross. The full-back miscued and almost put through his own net, Larrieu pulling off a reflex save to tip the ball away before diving to fingertip Cadamarteri's low drive round the post.
Cadamarteri finally beat Larrieu in the 70th minute twisting past Worrell before unleashing a fierce 25-yard shot that crashed against the post.
Friio pulled one back for the visitors in the 87th minute when he connected with a Lee Makel corner to head past Paddy Kenny but it was too little too late.