The Belgium international ran past five defenders before slotting home at Stamford Bridge on Monday.
Hazard scored both the goals as Chelsea won 2-0 against the Hammers in the Premier League.
Hudson-Odoi conceded that his team mate is so good that sometimes even his colleagues can do nothing but watch in awe.
“All I can say is that I watched the whole thing with my mouth wide open,” the England international said.
“He’s an exceptional player, though, and I do expect things like that from him.
“I just watch and learn from him in training, and then in games.
“Watching someone like that, he is a superb role model to look up to.”
Chelsea moved third in the table with Monday’s victory, edging ahead of Tottenham and Arsenal in the race for a top four finish.
Spurs and the Gunners have a game in hand over the Blues, though, leaving Hudson-Odoi aware of the importance of the win.
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“The three points were absolutely crucial,” the England international told Chelsea TV.
“A couple of other teams dropped points so we needed to get the result, and we did and we did it in the right manner as well.