Rather than saying Manchester United won Liverpool, a better choice of words would be Manchester United beat/defeated Liverpool. Or, Manchester United was victorious in their match with Liverpool.
If you insist upon using the word WON, it would be correct to say Manchester United won their match with Liverpool.
When the game ends with a score of 1 -1, you might say The Manchester United vs. Liverpool match ended in a 1 - 1 tie.
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