United were leading 4-3 with goals from Bruno Fernandes and Matheus Cunha in two minutes before Eli Junior Kroupi struck the final equaliser for Bournemouth.
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Reflecting on the see-sawing contest afterwards, pundit Carragher said on Sky Sports: "I think we've just seen the best game of the Premier League season so far and that's what makes the Premier League the greatest league, greatest product, whatever you want to call it, in the world.
"The majority of that game, Manchester United were absolutely fantastic.
"Bournemouth were not at the races at all in the first half, but they were fantastic in the second.
"What a game. Brilliant."