Manchester United seemed destined for an unwanted replay before Jesse Lingard again took responsibility, scoring a superb eighth goal in his past 10 appearances with six minutes remaining, which was followed by Romelu Lukaku sealing the win at the end of normal time.

José Mourinho’s side had appeared unable to kill off Derby County, as towards the close Marcus Rashford crashed the ball off the right post, Lukaku’s header hit the left, and Paul Pogba missed a sitter. Yet Lingard’s swerving long-range shot showed them how to do it and so United move on content.

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Of Lingard, whose season tally is now 11, the manager said: “He is in a clear evolution. He’s comfortable in the position he plays, improving with the progressive style of the team, which makes him feel even more like a fish in the water. He’s the opposite of Marcus because Marcus scores unbelievable goals in training and missed unbelievable chances in games. I’m not worried with Marcus because his good moment will arrive. Jesse won’t lose his stability. He’s mature, he understands the game better.”

Mourinho made five changes, drafting in Sergio Romero, Daley Blind, Chris Smalling, Henrikh Mkhitaryan and Rashford. Gary Rowett’s XI showed six different personnel from their previous match, the 1-1 draw with Sheffield United, with Tom Lawrence, Andre Wisdom, Alex Pearce, Sam Winnall, Marcus Olsson and George Thorne all selected.

United made a crisp start. Luke Shaw and Pogba moved the ball along the left. The Frenchman beat a Derby defender and switched possession to Lingard, who should have scored, instead lifting the shot over Scott Carson’s goal.

Yet following a flurry of United chances, the visitors stroked the ball around. Lawrence, the No10 in Rowett’s 4-2-3-1, broke up the middle and reversed play to Winnall but the centre-forward was stymied. The contest had an attractive flow. Lingard and Mkhitaryan put Rashford in and after a trick to create space the striker missed a glaring chance to open the scoring. Mata’s free-kick was saved well by Carson to his right and from the ensuing corner United found themselves back-pedalling. Mkhitaryan took this short and suddenly Shaw was passing back towards the centre-circle.

When the ball found its way to Johnny Russell he coasted down the left and found Martin Olsson’s head, the left-back forcing Romero to tip over. As the half-hour approached United became sloppy. Mkhitaryan gifted possession to Derby, Winnall raced forward and the Armenian was fortunate to see the attack fizzle out.

Facebook Twitter Pinterest Scott Carson stretches to save Juan Mata’s free-kick. Photograph: Jason Cairnduff/Action Images via Reuters

The same was true of United’s initial momentum: their display had flattened and they were now vulnerable. The lack of ruthlessness Mourinho can bemoan was evident when a Rashford glancing header from Mkhitaryan’s ball hit Carson’s left post. The No19 was at close range so had no excuse for missing. It was a repeat story when Mata picked him out and he could only head straight at the keeper.

As the interval neared United kept pressing. A Pogba free-kick drew “oohs” from the home support as Carson saved sharply to his right. Yet at the break the tie remained deadlocked.

Mourinho believed a change was required so Lukaku, who missed the win at Everton due to a head injury, replaced Mkhitaryan for the second half. The Belgian took his customary No9 berth, Rashford moved left and Lingard went in behind Lukaku.

Derby, though, made the brighter start. A Lawrence free-kick from the right found Tom Huddlestone who was unlucky not to score with a shot. From here United mounted a first attack of the period. Pogba and Lukaku combined and when the latter lost the ball he quickly claimed it back. Up stepped Herrera whose attempt was deflected for a corner.

This enlivened United. Pogba dug a route into Derby’s area and when the ball arrived at Mata’s feet he pulled the trigger and Carson beat the ball away. The passage reflected United’s dominance at the start of the contest.

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A Rashford corner from the left found Lukaku’s head but he could not direct it and the same player’s cross moments later was missed completely by Mata’s head.

All of this illustrated a troubling lack of requisite quality in the danger area and when Lawrence fired at Romero, who dived to his right, this was as accomplished as anything United had produced.

Mourinho’s men quickened the tempo yet a hint of desperation remained. Rowett brought on Matej Vydra for Winnall and Derby’s manager may have seen a credible replay move into sight. But Lukaku’s second confirmed victory and a potential warm weather break in Dubai.

According to Mourinho, this rests on Stoke City not drawing with Coventry City in their tie as United are due to face them on Monday week. If the Potters do have a replay then United’s league meeting with Mark Hughes’s side is moved to Saturday week and may curtail or even mean there is no trip.