The Red Devils were 1-0 winners against third-placed Tottenham Hotspur at Wembley last weekend thanks to Marcus Rashford’s 44th-minute winner.
Manchester United goalkeeper David De Gea had to make 11 saves to keep Tottenham at bay and help Solskjaer win his sixth successive game.
His predecessor Jose Mourinho often deployed negative tactics when Manchester United were pitted against their biggest rivals in the Premier League.
Former Chelsea FC boss Mourinho had a poor record against their traditional rivals during his two-and-a-half year rein at Manchester United as his negative tactics often led to negative results.
Solskjaer led Manchester United to four successive Premier League victories over Cardiff City, Huddersfield Town, Bournemouth and Newcastle United.
But the former Norwegian striker passed his first big test as Manchester United interim manager when his players were able to deliver three points.
Former Liverpool FC defender Carragher credit Solskjaer for restoring Manchester United’s confidence when it comes to games against their top-six rivals.
“For three or four years, watching Mourinho’s sides, in the big games, Manchester United were terrified going into them thinking they couldn’t compete with these other top teams,” Carragher told Monday Night Football on Sky Sports.
“They were terrified of what the opposition would do. Wingers were tracking the runs of opposing full-backs – how often did we say Manchester United were in a back six?
“This went on for years, I spoke to Gary Neville about it during Mourinho’s first season and he was convinced it would change when Mourinho got better players, it didn’t.
“The brilliant thing I loved from Manchester United at Wembley was that their fear had gone.”
Manchester United moved level on points with fifth-placed Arsenal following a return of 15 points from his opening five games in charge of the Red Devils.
The 20-time English champions will take on Brighton at Old Trafford in their next Premier League game on Saturday afternoon.
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