Lingard breaks the deadlock on 84′.
The Red Devils had more options up front, but their best chances were still falling to Rashford, who squandered a pair of opportunities after being put through by Pogba and Lingard, respectively.
Lukaku scored late to add gloss to the scoreline, but United had been far from impressive on the night.
Three minutes later, Pogba had a chance to send United ahead but his curling shot from just outside the box towards the top corner missed wide. Derby also created a scare as Martin Olsson rose higher to head Alex Pearce's corner but Sergio Romero tipped the goal bound header over the bar.
Tom Lawrence almost sent Derby ahead two minutes before the hour with a thumping shot from just outside the box but Sergio Romero made a brilliant save at the bottom corner. But Sam Winnall failed to profit as he dragged his shot wide.
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Rashford headed against the Derby post in the 34th minute, before heading straight at Carson three minutes later as the score somehow stayed goalless.
Carson was kept busy as he denied Pogba from a set-piece with the half winding down, while it was Derby who appeared the more lively side at the start of the second period.
On the other hand, the Rams are now unbeaten in their last seven matches and are second in the Championship with a fine shot of getting a chance to coming back to the Premier League.
The breakthrough would eventually come on 84 minutes, with Lingard unleashing a cracking effort from outside the box after a lay-off from sub Romelu Lukaku.
Lukaku, who showed no ill-effects following his return from a head injury, then doubled the home side's lead in the final moments when he converted after smart work from fellow substitute Anthony Martial.
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