Crystal Palace striker Black headed home Michael Tonge's cross midway through the first half after recalled Sky Blues forward Morrell had earlier put the visitors in front with his sixth goal of the season.
United almost made the perfect start when central defender Chris Morgan charged upfield in the second minute and saw his header come back off the woodwork.
But although Blades midfielder Alan Quinn threatened soon after - his right-foot curler from 25 yards whistled over - it was Coventry who made the breakthrough.
Michael Doyle's mis-hit shot flew to the unmarked Morrell in the penalty area and the recalled striker headed beyond home keeper Paddy Kenny into his bottom right-hand corner.
Stern John fired a shot wide from the edge of the penalty area as Coventry took charge, while Morgan sent another header over the crossbar.
But just as the visitors began to monopolise possession the Blades hit back to level after half an hour.
City keeper Luke Steele, who moments earlier had done well to parry a third header from Morgan, was caught flat-footed when Black powered home Tonge's fine cross from the left.
Kenny was alert enough soon after to hold Morrell's stinging drive from outside the area and then John's right-footer from closer in as the action swung from end to end.
Tonge let fly from 30 yards but could not keep it down as the first half ended all square.
Andy Gray went closest to breaking the deadlock after the restart, his 20-yarder held by Steele before steering the ball wide from close range.
Tonge rifled a 25-yard free-kick over the bar, Black tested Steele again with a left-footer from the edge of the box and followed up with another long-range effort as United created the better chances.
Paul Shaw twice went close to giving United the lead. His goalbound left-footer from the edge of the area was well-saved by Steele, while a right-foot effort from 18 yards flashed wide.
Steele then denied Tonge's header from Black's cross as the Blades pegged Coventry back.
But Coventry substitute Patrick Suffo almost snatched a late winner when his header from Doyle's ball in was saved by Kenny.
Quinn and Doyle traded long-range efforts in the closing stages, while Neil Warnock threw on youngster Kevan Hurst for Black with a last throw of the dice, but neither side made the breakthrough.