Substitutes Yannick Bolasie and Joe Mason both netted shortly after their introduction only for Richard Cresswell to put the hosts further ahead.
Jamie Mackie then struck late on for Paul Mariner's men to set up a nervy final five minutes but it was Ward's seventh and eighth of the season that ultimately proved the difference and made it 10 games unbeaten at home in all competitions for the south Yorkshire club.
Carl Fletcher crashed wide from fully 30 yards inside the opening three minutes for the visitors and Cresswell planted a firm header from a Ward corner past the post before the Blades surged ahead after seven minutes.
Clever play from Mark Yeates down the right channel on a swift counter attack paved the way for Camara to fire low into the bottom-left corner past David Stockdale from 12 yards.
It was Camara's second goal in as many home games and the Senegal international went close again moments later from just outside the penalty area.
Ward, Mackie and Rory Fallon then all spurned decent opportunities.
Reda Johnson will feel he should have forced Mark Bunn into action when he rose well to meet Craig Noone's corner just before the half-hour mark, but his header sailed over.
Stockdale kept out Ward's free-kick and denied Toni Kallio, but the Plymouth goalkeeper was powerless to prevent the hosts doubling their advantage with 10 minutes of the first half remaining.
Kallio crossed from the left wing and Ward dispatched a rasping 18-yard volley to take his tally for the season to seven.
Bunn saved Fallon's header moments later and Fletcher and Lee Williamson also went close before the interval.
A flurry of goals straight after the restart ensured the second half begun in pulsating fashion.
Ward first helped himself to his second of the afternoon after 47 minutes, making no mistake from 12 yards after being fed by Nyron Nosworthy out on the right flank.
But Plymouth substitute Bolasie pulled one back barely a minute later to give the visitors hope. Kari Arnason's right-wing throw eluded everyone and Bolasie capitalised on some hesitant defending to open his Argyle account.
A cross-cum-shot effort from Ward was kept out by Stockdale before Mason's first senior career goal left Bramall Lane stunned.
Chris Clark's cross was flicked on by Luke Summerfield and Mason was on hand to steer a low left-footed shot beyond Bunn after 56 minutes.
Ward, Camara and Cresswell all tried to give Kevin Blackwell's men some breathing space with decent efforts but to no avail, while Bolasie dragged wide at the opposite end from just outside the penalty area.
Cresswell was then rewarded for his endeavours 10 minutes from time as he seized on a defensive mistake and netted with ease.
But again Plymouth refused to throw in the towel and hauled themselves back into the game after 85 minutes courtesy of Mackie's emphatic 20-yard volley.
Source: Team Talk
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