The pounds 12.5m striker, who scored in the dying seconds against Charlton and Liverpool in United's last two matches, struck relatively early, after 65 minutes, to crank up the pressure on teams trying to stay with them in the championship marathon.
It was Yorke's 19th goal of the season and his seventh in five matches in which United have built a fair head of steam. Six successive wins is an emphatic response to a December of doubt and too many draws.
The response since the turn of the year has been points perfect but there was one thing to mar Alex Ferguson's delight: an injury to Ryan Giggs that will almost certainly force him to miss United's European Cup quarter- final against Internazionale.
The Welsh winger lasted only 10 minutes before having to leave the field with a hamstring injury, a worrying echo of last season when an identical problem, also incurred against Derby in February, was identified by Ferguson as a fundamental reason for United's failure to win a trophy. It was the reason why he bought Jesper Blomqvist from Parma in the summer.
"A hamstring is a hamstring," Ferguson said grimly. "He'll be out for several weeks. It makes him very doubtful for the Inter matches. He felt a wee tweak. We don't know how severe it is, but we'll put ice on it and see tomorrow."
Giggs' injury was a major dampener on an otherwise good night for United under troubled circumstances. They got the win Ferguson had demanded but it was by no means a straightforward victory, and for much of the night the home side were thoroughly confounded by Derby's tactics.
Jim Smith adopted a 3-4-3 formation that changed to 3-6-1 as Darryl Powell and Kevin Harper dropped deep when the need arose. That clipped United's wings, forcing them towards a packed centre where Horacio Carbonari, Igor Stimac and Spencer Prior were waiting.
It says much for the Derby defenders' performance that United were largely reduced to firing shots from long range, the first which was an absolute screamer from 30 yards from Jaap Stam after four minutes. Russell Hoult saved that with difficulty but it was by far United's best effort in a first half that was more puzzle than solution for the home side.
Indeed, Wanchope almost put the visitors ahead after 22 minutes. Lars Bohinen flicked a delightful pass forward, the Costa Rican controlled with his chest and then shot low to Peter Schmeichel's right, finding the side netting instead of the goal.
United pounded forward after the break without reward and they were becoming increasingly anxious when Yorke finally found a way past Derby's defensive towers. Inevitably the route was central, but this time Nicky Butt's looped pass was neither intercepted nor was Yorke's run offside, and he tucked his shot just inside the post.
Derby had to abandon their entrenched positions and Carbonari almost got them a reward with a bicycle kick that would have troubled Schmeichel if he had made proper contact. Instead the touch was not true and it looped high enough for the goalkeeper to recover.
As the play stretched United, too, had their chances and Yorke seemed certain to get a second when Blomqvist's pin-point cross located him at the far post. Hoult saved that at point-blank range - but the damage had been done.
Manchester United (4-4-2): Schmeichel; G Neville, Johnsen, Stam, Irwin; Scholes, Keane, Butt, Giggs (Blomqvist, 10); Yorke, Solskjaer. Substitutes not used: P Neville, Cole, May, Beckham.
Derby County (3-4-3): Hoult; Prior, Carbonari, Stimac; Laursen, Bohinen Carsley, Dorigo; Harper (Burton, 70), Wanchope, Powell (Hunt, 79). Substitutes not used: Knight (gk), Schnoor, Christie.
Referee: S Lodge (Barnsley).Reuse content