The Rams were sent spinning to their third defeat in five matches at Pride Park.
Blades striker Cresswell converted Jean Calve's cross from close range in the 15th minute and the only surprise was that the visitors failed to add further goals in a game they dominated.
Ched Evans, Cresswell and Nick Montgomery all spurned chances to add to Derby's woes, while Nigel Clough's side had only two notable efforts on goal, both from Kris Commons in the second period.
Derby, without a win since their triumph at Leeds on the opening day of the season, made just one change to the side that conceded two stoppage-time goals to draw 2-2 with QPR in their last match, with Tomasz Cywka assuming duties as a lone striker in place of Conor Doyle.
United, unchanged after clinching their first win of the season under manager Gary Speed against Preston two weeks ago, began full of confidence and went close through Evans before taking a 15th-minute lead.
French defender Calve, whose long-range winner on his debut stunned Preston, wasted little time in making another telling contribution, sweeping over a cross from the right into the path of Cresswell, who made no mistake from six yards.
Derby had plenty of first-half possession, but the Blades carved out by far the better chances.
Evans' low left-footed shot was parried by Derby goalkeeper Stephen Bywater and summer signing Johnny Ertl pulled his effort wide moments later.
Evans and Cresswell again, with a header from another Calve cross, went close to doubling the visitors' lead before the break, while Blades goalkeeper Steve Simonsen did not have a save to make in the first period.
Commons had Derby's first effort on goal 80 seconds after the restart, but his angled drive was blocked by Blades midfielder Montgomery.
Evans continued to make a nuisance of himself, firing wide and testing Bywater with another angled shot, either side of Derby manager Clough's decision to send on new signing Alberto Bueno in place of Robbie Savage to help ease the burden on Cywka.
Bueno, on a season-long loan from Real Valladolid, was given a crude welcome to English football soon after when Nyron Nosworthy clattered into the 22-year-old Spaniard and received a booking.
But United continued to carry the greater threat. Calve crossed again, this time for Jamie Ward to plant a firm header just wide in the 69th minute.
Cresswell lashed a shot over the crossbar and Montgomery dragged another wide before Commons forced Simonsen to hold his raking 20-yard shot.
Ward was off target with another shot as Derby failed to lift themselves for a rousing finale and it was Cresswell who went closest to adding to the scoresheet in the five minutes of time added on when he rifled a 20-yard effort over the crossbar.