Bamford set the Whites on their way to a comfortable victory at Elland Road, but the use of his elbow left the Millers raging.
The one-cap England international appeared to use his arm to divert a deflected cross from Junior Firpo into the net after ten minutes.
With no VAR in the Championship, Bamford gleefully wheeled away in celebration with his gesture unnoticed by referee Andy Madley and his assistants.
The striker then rubbed salt in the wounds of the second-tier's bottom club by jumping up and flinging his elbow out to fans.
A double from Crysencio Summerville sealed the three points, but the incident left Rotherham boss Leam Richardson raging, particularly when Bamford admitted his handball.
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Millers manager Richardson then hit out at the officials for then joking with the ex-Chelsea forward afterwards.
Speaking after the match, Richardson said: "The first [goal] was disappointing, I think it's an easy decision, but officials have a million and one decisions.
"Andy [Madley] has apologised, I didn't really enjoy the linesman on this side laughing and joking with Patrick Bamford, that's unprofessional.
"I don't want to guess, but I think it's unprofessional to joke with a player who has cheated them out of a decision and potentially a result as well. That's for them to take forward."
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Richardson added: "If our striker had put his arm forward and nicked a goal, would I tell him to go to the ref and chalk it off? Probably no.
"Half-time, he apologised because he wasn't fully committed to the decision, he didn't want to guess. He spoke to Patrick and he said yeah it hit my arm and went in.
"It always seems to come around at these places but we'll move on."
It wasn't just Bamford who saw the funny side of his goal, with Leeds fans also joining in on the joke as they likened it to Maradona's 'Hand of God' goal against England at the 1986 World Cup.
One posted on X, formerly known as Twitter: "Bamford channelling his inner Maradona with that goal FFS we move!"
Another posted: "Bamford nearly recreating the hand of god."
A third added: "Maradona would have been happy with that goal!"
The result meant Leeds moved back up to third spot in the Championship, only one point adrift of Southampton in the second promotion spot, albeit having played a game more.
Rotherham meanwhile remain rock bottom of the table with just one win in their last 19 league meetings.