Marcus Rashford was the guiltiest party in the first half with a poor point-blank header that he tamely nodded against the post.
But Jose Mourinho's side never gave up, with Lingard finally finding the back of the net in the 84th minute after a superb strike from outside the box into the top corner of the net.
Gary Rowett's men burst forward in search of an equaliser and were caught in stoppage time on the break when Anthony Martial combined with Lukaku to double United's advantage. The top two teams in the Championship table at the end of the season are promoted to the Premier League, while the third-sixth place teams compete in a playoff for the final spot.
Marcus Rashford was presented with the best chance of the half as a fortunate bobble gave him space to pull the trigger towards goal, but he fired his shot just over the bar - the shot should've hit the target, and if it did, would've given the hosts a deserved lead.
United also got good news regarding Romelu Lukaku, as the Belgian worldwide will be fit and available to play after suffering a scary blow to the head against Southampton on December 30.
Romelu Lukaku, who had replaced Mkhitaryan at the break, then had his goal-bound shot blocked as Pogba curled off target in a good spell of attacking intent from United.