Manchester United beat Chelsea 2-1 at Old Trafford, coming from behind with goals from Romelu Lukaku and Jesse Lingard.
Blues star Hazard was taken off with 20 minutes of the game remaining, just two minutes before Lingard scored the winner.
Chelsea manager Antonio Conte claimed Hazard’s withdrawal was due to him being tired.
But Moreno says United’s victory hopes were boosted massively when Hazard went off, and so it proved with the result.
“I’ll put it to you this way, if you’re a Manchester United player and they put the number up and they see Eden Hazard go off the field, what is their reaction?,” the former Major League Soccer star said on ESPN FC.
“It’s like ‘alright, well we don’t need to chase that guy around’.
“That guy’s a threat, that guy can change a game.
“The guy coming on for him I don’t think can change a game the way Eden Hazard can.
“So as a Manchester United player I’m thinking ‘yeah, alright, we’ll take this and this allows us to be a little bit more aggressive in the way we approach the game, maybe we can take some more chances going forward because we don’t have to worry about that guy catching us on the counter’.”
Chelsea dropped to fifth in the Premier League table following the defeat.
London rivals Tottenham sit fourth, two points clear of Conte’s side.