On a day when José Mourinho and Paul Pogba’s relationship hit rock bottom came a testing night for the Portuguese as Derby County knocked Manchester United out of the Carabao Cup.

Phil Jones saw his kick saved by Scott Carson and given Mourinho’s ongoing discontent with Pogba, plus a defeat that adds to United’s drift, the manager will come under further scrutiny.

Jack Marriott’s late header had been answered by Marouane Fellaini’s in injury time after United had ceded the initiative following Juan Mata’s early goal. In the second half a Harry Wilson equaliser was followed by Sergio Romero becoming the third United player in five matches to receive a red card – for handling the ball outside the area on 67 minutes – before Fellaini’s intervention seem to have saved home blushes.

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This was a famous win for Derby and a particularly sweet one for the manager, Frank Lampard, who spoke before of his admiration for Mourinho, under whom he enjoyed glittering success at Chelsea.

Mourinho made nine changes, retaining only Romelu Lukaku and Jesse Lingard from Saturday’s draw here with Wolves. Pogba was among those missing, although he was one of a number of players the manager stated was rested.

Lampard’s XI was the same as that beat Brentford 3-1 last time out yet any hope of a famous win was dented after three minutes following a flowing move.

Anthony Martial showed his class with a neat first touch and raced down the left. A cross was flicked on by Lukaku, Lingard dummied, and Mata swept past Carson.

The perfect start for United came close to being matched by Derby. As United dawdled Mason Bennett’s effort required a fine save from Romero.

Next came a moment of United quality. Ashley Young, wearing the armband, pinged in a sweet 40-yard pass that bypassed the visiting defence and landed on Mata’s toes. The No 8 killed the ball but could not beat Carson and a corner from the left ensued.

Young took this and saw his delivery ricochet off Carson’s right post in a fortunate escape for Derby. The sense of an open contest in which United might streak ahead at this point was confirmed when Richard Keogh made a serious error in front of Carson. He gave the ball away to Lukaku, yet after racing in on goal his attempt went wide. Derby’s response came via a Keogh advance from the back but the central defender’s 20-yard shot missed to Romero’s right.

Martial was unlucky to be dropped for the Wolves game following an eye-catching display against Young Boys and he was in effervescent mood again here. After skipping to near the left byline he crossed and Lukaku might have doubled the lead but the centre-forward mistimed his jump and over went the header.

Facebook Twitter Pinterest Harry Wilson – on loan from Liverpool – celebrates after his stunning free-kick against Manchester United. Photograph: Paul Ellis/AFP/Getty Images

Keogh continued to make errors. Just before the half-hour the captain dawdled and looked to have given possession away again in the danger zone but he managed to recover. Unlike Lampard, who stood throughout the opening period, Mourinho waited 31 minutes before leaving his seat and when he did this was to remonstrate at some lax play from the team. The Portuguese was also frustrated that United had not been more ruthless – a regular refrain of his – as at the break their lead remained just the single goal.

As this juncture neared Martial advanced and looked to thread the ball to Lukaku who lurked near the penalty spot but he lacked precision just as the side had thus far lacked the killer edge.

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The second half began with Lukaku having to head clear a Derby free-kick and Romero hitting a regulation clearance against an opposing player and the visitors winning a corner moments later.

This United performance was beginning to be reminiscent of Saturday’s slipshod display and of so many under Mourinho. Derby were becoming the ascendant side and Romero was again required to protect the lead as more schoolboy marking allowed Wilson in though the wide man could not beat the Argentinian.

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United were unable to get hold of the ball and dictate the contest and when Johnson flew into Martial with a tackle near halfway this summed up how much more urgent Derby were.

This all pointed to what came on the hour. Wilson, a Liverpool loanee, stepped up to take a 30-yard free-kick that he curled from right to left, sending Romero the wrong way for a memorable equaliser.

Mourinho reacted instantly. He took off Lingard and Ander Herrera for Fred and Fellaini yet the travelling support’s own response was to inform the 55-year-old he was “getting sacked in the morning”.

Now came disaster for United as Romero was sent off by the referee, Stuart Atwell, for handling outside the area as Wilson raced on to the ball. This meant Lee Grant – who played for Derby for 11 years in two spells, with more than 170 appearances – entering for his United debut at the age of 35 to set up a frantic finish, which included one fine save.

Now came the final whistle, Mourinho’s misery and Lampard’s joy. The latter said: “I’m shell-shocked. To go down early at Old Trafford and play as well as they did was superb. I am a proud manager. It was the easiest selection I have had. The players were superb against Brentford and they deserved the chance to play at Old Trafford. I wanted to bring a team who could really compete.”