United dominated possession and enjoyed more shots than Palace — 11 in the first half alone — but a goal proved elusive for much of the match.
However, Fred’s strike from the edge of the box in the 77th minute settled the contest and moved United up to 6th in the Premier League table.
The goal came shortly after Palace had squandered its best chance of the match when Jordan Ayew couldn’t turn a shot into the net following a corner.
“With one training session and quite a few conversations with the team … what they did today, defensively, we had full control of the game,” Rangnick told beIN Sports
after the match.
“Maybe one or two situations where it was a little bit dangerous, but apart from that we had full control of the game … In the end, we deserved to win,” he said.
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United sacked manager Ole Gunnar Solskjaer two weeks ago, with Michael Carrick taking over as caretaker manager.
Rangnick, previously head of sports and development for Russian club Lokomotiv Moscow, was then named as the club’s interim manager until the end of the season, after which he will stay at the club in a consultancy role for a further two years.
Since parting ways with Solskjaer, United has won three and drawn one of its past four games, most recently a thrilling 3-2 victory against Arsenal on Wednesday.
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United is one point behind 5th-placed Tottenham Hotspur in the Premier League table. The north London side defeated Norwich City 3-0 on Sunday thanks to goals from Lucas Moura, Davinson Sanchez and Son Heung-min.