The visitors looked likely to force a replay before Lingard struck with a first-time shot in the 84th minute for his fourth goal in as many games after a fine brace in a 2-2 Premier League draw with Burnley and another in a 2-0 win over Everton.
Marcus Rashford was next to come close for United in the 18th minute after driving into the Derby box, but the attacker just missed the crossbar, before Derby goalkeeperScott Carson kept out a curling free kick from Juan Mata. They changed players as the Championship is important to them.
The visitors' starting line-up confirmed Gary Rowett's predominant focus on the Championship this season, where his side are vying for automatic promotion to the Premier League and now sit in 2nd place.
England midfielder Lingard let fly from outside the area with six minutes remaining for his fifth goal in his past six outings to finally break the resistance of the spirited Rams.
Derby County made a very strong start to the second-half and were clearly growing in confidence; but still living dangerously as Mata, Lukaku and Pogba all had shots saved, blocked and fired narrowly wide respectively five minutes after the restart.
At the other end, Marcus Olsson's clever flicked header from Johnny Russell's left-wing cross forced Sergio Romero into his first action of the evening.
Lingard and Paul Pogba both had early attempts for a United team that started on the front foot at Old Trafford.
In the second half, Jose Mourinho introduced Romelu Lukaku hooking off Henrikh Mkhitaryan in the process but it was Derby who came close to scoring.
Manchester United are 2/9 favourites to win this FA Cup match whereas Derby are massive odds - 13/1 to win at Old Trafford.
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