Paul Ifill added a second to put the Bramall Lane side in control as they chased their ninth straight win of the season to keep their four-point lead intact before ex-United favourite Paul Peschisolido came off the bench to snatch an eye-catching goal and set up a nail-biting finish.
The high-flying Sheffield side broke the deadlock on seven minutes. Unsworth's curling corner from the right should have been cut out by Danish midfielder Morten Bisgaard but he failed to head clear as the ball dipped over the line.
Tommy Smith saw his low drive smothered by Paddy Kenny before carving out a half-chance, weaving his way into the area before being stopped by the United keeper who darted out to save at his feet.
The Blades were in total control and threatened to over-run hard-pressed Derby. Neil Shipperley was foiled by Rams keeper Lee Camp who palmed away the big striker's close-range header before United struck again in the 37th minute with Unsworth again involved.
The former Portsmouth defender's corner was headed back by Shipperley before being cleared to the lurking Ifill who pounced from 14 yards, his low drive taking a slight deflection past the stranded Camp.
United, looking for a third to kill off the Pride Park side, carved out a half-chance minutes after the restart, Ifill sweeping a right-foot cross to the waiting Alan Quinn whose right-foot shot from the edge of the area was deflected wide of the far post
Derby battled their way back into the game in the 54th minute, 34-year-old Peschisolido producing a quality strike from close range.
Smith sparked the move threading the ball to Peter Whittingham and Peschisolido , on at half-time for the ineffective Stern John, took the ball in his stride before stroking it with the outside of his right foot past Kenny from six yards.