And there were more groans than cheers at Bramall Lane after former Celtic and Wigan striker Camara had fired the home side ahead three minutes before half-time.
Bottom club Peterborough failed to mark manager Mark Cooper's first game in charge with their first away win in the league this season, but will feel they deserved a point.
Cooper's new charges were under the cosh for long periods of the first period, but created a string of chances after the break and were denied by Blades goalkeeper Mark Bunn, who saved George Boyd's 66th-minute penalty.
Blackwell handed a first start to summer signing Lee Williamson as well as Camara, who also made his first appearance in the starting XI, while striker Aaron McLean returned to Peterborough's starting line-up.
Posh midfielder Boyd fired a left-footed shot wide from 25 yards and team-mate Chris Whelpdale was off target from similar distance, but the Blades were in control for long spells in the first half.
Home striker Ched Evans hit the crossbar from Jamie Ward's outswinging corner in the 25th minute and then had a second effort from close range that was blocked by Posh midfielder Toumani Diagouraga.
Morgan headed another corner from Ward wide and although Mclean tried his luck from outside the box for the visitors, the Blades were rewarded for their dominance when Camara slammed the ball home from 12 yards after Evans' shot rebounded back off the legs of Posh goalkeeper Joe Lewis following Ward's cross.
Camara was foiled by another block from Diagouraga straight from the kick-off and Andrew Davies headed Morgan's ball into the area just wide in the first-half's closing stages.
Peterborough responded after the interval, going close with Boyd's header from Scott Griffiths' ball in, while at the other end Camara went close to grabbing his second when he headed Kyle Walker's cross over the crossbar.
The visitors then stepped up the tempo and had three efforts on target in the space of three minutes.
McLean's 20-yard shot was held by Blades goalkeeper Mark Bunn, who then caught Craig Mackail-Smith's effort from inside the box.
Mackail-Smith then headed wide as Peterborough pressed for an equaliser before the Blades enjoyed the kind of luck that has deserted them in recent weeks.
Blades defender Davies fouled Mackail-Smith in the area but after Hertfordshire referee Grant Hegley had pointed to the spot, Boyd's power penalty was brilliantly save by goalkeeper Bunn.
But still Peterborough chased an equaliser and Boyd went close to redeeming himself four minutes later only for Bunn to foil him again by holding on to his volley.
Blades midfielder James Harper could have killed the game, but mis-hit his shot with the goal beckoning from Walker's smart cutback, while Peterborough were becoming increasingly anxious after failing to convert their second-half chances.
Posh pair Charlie Lee and Ryan Bennett were both off target with long-range shots and Shaun Batt drilled a 25-yard shot wide in stoppage time.