The fan ran onto the field of play and confronted Howe in the closing stages of the match, with the scores level at 2-2.
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The pitch invader pushed Howe, who reacted angrily, before stewards intervened and ejected him from the ground.
Magpies assistant Jason Tindall was among those to chase the man away from the sidelines.
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Speaking to talkSPORT after the match, Howe said: "For me, I've never experienced that before.
"So I was looking in the opposite direction and he ran on and shouted something at me that I won't repeat.
"It was over in a flash but it was the last thing you expect in that moment and it's alarming for football really because we can't have that.
"The safety of everyone, coaching staff, players, is of paramount importance."
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Leeds released a statement on the incident and said: "Leeds United can confirm that following an incident at our Premier League match against Newcastle United today, an arrest has been made and a lifetime ban has also been issued."
A statement from West Yorkshire Police added: "Police have charged a man with assault and entering the field of play following an incident at Elland Road football stadium during the Leeds United versus Newcastle United football match yesterday (13/5). The man has been bailed to appear before magistrates on 21 July."
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"Eddie Howe has done absolutely nothing, for a start, but also he should feel safe in his technical area, that is disgusting behaviour."
England legend Stuart Pearce added: "I'm not sure what goes through people's minds at times. It's an emotional game, I understand that but, my goodness, please."
A hot-tempered clash ended all-square after three penalties and a red card.
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Leeds took the lead through Luke Ayling but failed to double their advantage when Patrick Bamford missed from the spot.
Moments later, Newcastle were awarded a penalty and Callum Wilson made no mistake.
The Magpies striker put the visitors in front with a second effort from 12 yards before Rasmus Kristensen salvaged a point for the hosts.
In the dying stages of the game, Whites full-back Junior Firpo was sent off for a second yellow card - which is when Howe was confronted by the angry supporter.