Blades striker Cresswell swept home Glenn Little's cross two minutes after the interval, but victory has done little to resurrect the South Yorkshire side's play-off chances.
Kevin Blackwell's side began the day nine points adrift of the top six after winning only one of their previous nine league games and this encounter against another team struggling for form - Coventry are without a win in their last eight matches - provided limited entertainment for a crowd of 23,603.
Coventry, whose last success was at relegated Peterborough on March 6, raised their game after falling behind but failed to carve out any clear-cut chances.
Little and on-loan Derby defender Paul Connolly were recalled by United manager Kevin Blackwell and Scotland international Gary Naysmith, yet to appear for the Blades this season after two long-term knee injuries, returned to the substitutes' bench.
Martin Cranie, Richard Wood and Carl Baker were all back for Coventry.
The Blades had only two headers from Darius Henderson to show for their early dominance, the first flying wide and the second comfortably held by Coventry goalkeeper Keiren Westwood.
Little's shot from inside the penalty was then blocked by visiting defender Leon Barnett, but there was little else to excite the Bramall Lane crowd in the first period.
Coventry had to wait until the 31st minute before Clinton Morrison headed their first chance straight at home goalkeeper Steve Simonsen, while Blades striker Richard Cresswell's similar effort from Little's corner was comfortably held by Westwood.
United stepped it up towards the break, with Andy Taylor firing straight at Westwood and Henderson volleying wide from 25 yards before City striker Freddie Sears' overhead kick was easily snaffled by Simonsen.
Westwood saved easily from Blades defender Chris Morgan's far-post header just before the interval, but the home crowd were given some cheer two minutes after the restart.
Little broke clear down the right and his fine ball into the penalty area picked out Cresswell, who swept the ball home into the top corner from 12 yards.
Blades midfielder Stephen Quinn's volley was then blocked and Little pulled his shot wide from inside the area.
The visitors responded and Coventry's Sammy Clingan curled a 25-yard free-kick inches over the crossbar, Baker forced Simonsen to hold his drive from outside the area and Wood headed just wide from a corner.
Eastwood, with a right-footed volley from 20 yards, and Clingan, from inside the area, peppered the Blades goal as the visitors pressed for an equaliser, but failed to seriously trouble Simonsen.
Mark Yeates, on for the hard-working Quinn, went close to doubling the home side's lead from close range in the closing stages but his shot hit Barnett, while at the other end Aron Gunnarsson's 25-yard drive whistled over the crossbar.
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