The Brazilian forward dropped to his knees in delight before kissing the Red Devils badge as United ran out 4-2 winners away in Wales.
A huge scare was on the cards after League Two outfit Newport came from 2-0 down to level things up at Rodney Parade.
Goals from Bruno Fernandes and Kobbie Mainoo inside the opening 13 minutes saw Erik ten Hag's side threaten to run riot.
But goals from Bryn Morris and Will Evans saw Newport get back on level terms, leading to cries of 'You're getting sacked in the morning' aimed towards Ten Hag from the home fans.
However they couldn't force themselves in front, with Antony, who assisted Fernandes for his opener, reacting quickest in the box after Luke Shaw's shot came off the post.
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He was on hand to tap into an empty net in the 68th minute from the edge of the six-yard box to bring an end to his 31-game goal drought.
In what was his 23rd outing this season in all competitions, the relief on Antony's face was there for all to see.
Though talkSPORT host and ex-Aston Villa striker Gabby Agbonlahor was less than impressed by Antony's reaction.
Taking to X, he said: "Antony kissing the badge like he's scored against Real Madrid. I think he's found his level to shine."
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And Rasmus Hojlund then secured the victory in the fourth minute of stoppage time to bring up his eighth goal this term.
The result means that last year's finalists will now face either Bristol City or Nottingham Forest away in the fifth round.
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Speaking after the six-goal thriller, United skipper Fernandes expressed his frustration over his side's performance.
He told the BBC: "Obviously it was not the result that we wanted, we got the win that we wanted, but the result was not the perfect one for us.
"We didn't want to concede goals, the first one was great from them, an unbelievable shot.
"We had chances to make the 3-0, but when you get 2-0 in these type of games, everyone wanted to score and get their goal and everything and sometimes we don't get the best decision for the team.
"I think after we did a great job to close the game."