It took them an hour to do it, but they did eventually overcome the plucky League One outfit thanks to goals from Carrick, Herrera and Rashford.
It hadn't been the best of weeks for Mourinho and his men as three successive defeats had cast a shadow over the club and raised questions about some of the player's commitment to the cause.
Disaster is too strong a word to be used at this early stage of the season. However, a defeat in the EFL away at Northampton would have had alarm bells ringing.
Only two players Smalling and Rooney kept their places in the starting XI: Romero, Fosu-Mensah, Smalling, Blind, Rojo, Schneiderlin, Carrick, Memphis, Herrera, Young and Rooney.
The United captain had been chosen as the main striker and Mourinho expected only one thing from him and that was goals and if he didn't deliver there was a strong bench including Ibrahimovic and Rashford.
Rooney had the first clear chance of the game with a weak shot inside the area. United won the first corner of the match after a couple of minutes from a deflected shot by Herrera.
It was Rooney again, who was guilty of missing an open goal after a cross was played into the danger area from the right. The skipper inexplicably side-footed his effort wide when it seemed easier to tuck the ball away.
The away side were awarded a free kick inside the area after the home side were guilty of a back pass just before the twenty-minute mark. Depay rolled it into the path of Rooney, whose shot was blocked by the wall only for it to find Carrick loitering on the edge of the area.
He calmly hit the ball first time and managed to send it flying into the top corner of the net. That was Carrick's first goal since March 2015 and a welcome one it was too.
Rooney had a headed goal ruled for offside on the half hour after Fosu-Mensah had seen his effort rebound off the bar.
United didn't have it all their own way however, as the home side almost pulled level with a cracking drive from former red academy player Gorre that stand in keeper Romero had to push over the bar.
In fact, it was Northampton who pulled their socks up and began to find another gear as they piled on the pressure and it paid off five minutes before the break when they won a penalty after Blind clumsily brought down Hoskins after a combination of Rojo, Fosu-Mensah and Schneiderlin failed to clear the ball from their own area.
Revell stepped up and sent Romero the wrong way to level the scores and gave Mourinho plenty to think about during the break.
Northampton got the second half underway with Mourinho deciding against making any changes at the restart.
The home side were put on the back foot by the Red Devils as Young tried his best to create openings down the right flank.
It only took Mourinho ten minutes to change things around with Rashford replacing defender Fosu-Mensah and Ibrahimovic coming on for the hapless Memphis, which meant Young switched to the wing back position to make way for the forwards.
As the match entered the final twenty minutes player of the night Herrera finally found the back of the net after he hit a brilliant right-footed drive that gave the keeper no chance and handed the visitors the lead.
Fellaini entered the fray for the last fifteen minutes in place of Schneiderlin to offer a different variety to the play.
It was Herrera, who from the half way line hooked a hopeful ball high into the air and as it fell from the skies it looked, for all intents and purposes a routine clearance for keeper Smith, but as he raced out to the edge of his area there was Rashford bearing down on him at speed.
The sight of the young forward rushing towards him caused the keeper to panic and he completely mistimed his attempted clearance and Rashford reaped the rewards and blasted the ball gleefully into the empty net.
United saw out the game and in the end dispelled any talks of a crisis to book a place in the next round which threw up a mouth-watering home draw against Manchester City and an early opportunity for Mourinho to gain revenge over Guardiola.
Even with the win, Mourinho will know that some of his players underperformed once again with Rojo the weakest link in defence and up front Memphis failed to impress and one has to wonder how long the manager will put up with the winger.
Not for the first time in his fledgling career, Rashford had a huge impact on the result with an assist and a goal of his own as his eagerness showed the older heads how pure enthusiasm can change a game in an instant.
The hope for the future is that he never loses that desire to play the game as it should be played when others around him have forgotten as they have aged.
One player who did roll back the years with an assured performance in midfield was Michael Carrick. His contribution proved that he still has what it takes as long as he gets enough rest and before people get carried away it was against lower opposition, so the question will be whether or not he can sustain that level on a regular basis in the Premier League.
Next up is the visit to Old Trafford of the current champions Leicester City who United defeated in the Community Shield last month. However, we can expect a different type of game at the Theatre of Dreams.
Until then thanks for reading.