The former Wigan striker found the target four minutes before the break before the basement side missed a penalty as the Blades picked up their first win in eight games.
Peterborough,who are finding life tough after promotion from League One, held on as United applied the pressure.
James Harper and Camara both had shots blocked as they wriggled free into the area.
But United were caught out as Harper dallied on the ball and goalscoring midfielder George Boyd quickly nipped in and took a stride before drilling in a low strike from 20 yards.
The ball flashed inches wide of the far post as Mark Bunn scrambled across his line.
Stuttering United almost snatched the lead in the 25th minute after winning a corner on the right.
Fit-again Jamie Ward cleverly picked out £3million striker Ched Evans, who lashed in a stinging right-foot shot which hit the underside of the bar and bounced clear.
The basement side, under strict instructions to get players behind the ball, had the pace to hit United on the break.
Kyle Walker, on loan from Spurs, was caught in possession by full-back Scott Griffiths, whose measured pass found Craig Mackail-Smith 15 yards out but the striker dithered as Matt Kilgallon cleared.
United broke the deadlock four minutes before the break when the hard-working Ward cut in from the right to pick out Evans and his low shot was blocked by the legs of Joe Lewis as Camara followed up to slot the ball past the stranded keeper.
He could have had a second as Lee Williamson and Walker exchanged passes. The United defender's cross was met at the far post by Camara, who was stretching as he headed over from six yards.
United escaped in the 66th minute when Aaron McLean's back heel found Craig Mackail-Smith, who was brought down by Andrew Davies' clumsy challenge.
However, Boyd's penalty was a poor strike and Bunn dived to his left to smother the ball.