Preston had their moments in a tight Championship contest on Saturday, but a second-half pile-driver from the French defender was enough to hand Gary Speed his first win as manager.
United can look forwards but Darren Ferguson’s North End have now lost three of their opening four games and are without a win on the road since January.
Calve and Stephen Jordan made their bows in a United defence that was missing skipper Chris Morgan through injury.
Former Blades midfielder Keith Treacy lined-up for Preston and after his spectacular extra-time winner in the midweek Carling Cup tie against Bradford, he caused the home side some discomfort in the opening stages.
Following an early sighter, Treacy rattled the crossbar with a third-minute free-kick.
Calve then showed he was not afraid to come forward from right-back to try his luck from distance, and speculative long-range efforts proved to be the order of a cagey half.
Preston regularly fell behind the ball to stifle spells of United pressure before exploiting the pace of on-loan Manchester United striker Joshua King on the counter attack.
In first-half stoppage time North End’s David Gray whipped in a cross that narrowly evaded Paul Hayes moments after a similar delivery from Calve had flashed wide of Andy Lonergan’s upright at the other end.
The second period began with Preston exhibiting the brighter football once more and they created the first clear-cut opening of the contest.
King got the better of Nyron Nosworthy and burst into the penalty area to force a save from Steve Simonsen. From the rebound Billy Jones blazed over.
Treacy then left the field injured to be replaced by
Danny Mayor, but it did not interrupt Preston’s rhythm.
The danger came from King once more, this time via a rasping 30-yard effort that Simonsen stretched to cling on to.
Mark Yeates replaced the ineffective Ched Evans up front for United and his stinging 63rd-minute drive was pushed away impressively by Lonergan.
The Blades were enjoying their best spell of pressure in the match and with 17 minutes remaining Calve marked his debut with a goal fit to win any game.
The on-loan Nancy full-back cut inside 35 yards from goal before unleashing a speculative effort into the top corner.
Calve bizarrely emerged from his goal celebration with cramp and was immediately replaced by Matthew Lowton.
Jon Parkin came on for Hayes as Preston pushed for an equaliser and the burly frontman thought he had won a penalty for his side three minutes from time.
But referee Iain Williamson adjudged Kyle Bartley’s foul to be outside the penalty area and Paul Coutts drilled the resulting free-kick into a well staffed United wall.