Play was halted for seven minutes at the beginning of the second-half as the protester entered the field at the Gwladys Street End.
The security team at Goodison Park required a pair of wire cutters to free the protester before he was led out of the stadium.
Thirteen minutes of stoppage time was added, where 10-man Everton found a 99th-minute winner via Alex Iwobi’s strike.
It condemned the Magpies to a second defeat in a row, though they do remain nine points above the Premier League zone ahead of a lengthy break.
Asked about the incident, Eddie Howe said: “No, never seen anything like that. I didn’t realise what was happening to start with.
“There was a big delay and I don’t know whether that affected us. I’m not using that as an excuse.
“Second half, we weren’t the same team.”
A statement from Merseyside Police on Thursday evening confirmed the man’s arrest.
It read: “We can confirm a man was arrested after encroaching on to the pitch during the Everton v Newcastle United Premier League fixture.
“At around 8.55pm it was reported that a man disrupted the match by running on to the pitch and tying himself to the goal post at the Howard Kendall Gwladys Street End.
“The suspect, a 21-year-old man, has been arrested on suspicion of pitch encroachment and he is now in police custody. The game resumed and has now concluded.”
The protester was raising awareness for ‘Just Stop Oil’, who are concerned about new oil fields in the North Sea.
A statement from Just Stop Oil read: “At 8:50pm today, a young supporter of Just Stop Oil ran onto the pitch during the Everton vs Newcastle United game to draw attention to the group’s demand that the Government ends all new fossil fuel supply projects.
“Louis, 21, locked on to the goalpost at Goodison Park wearing a Just Stop Oil t-shirt, causing the referee to briefly stop play.”
Attached to the statement, Louis added his own message: “It’s 2022 and it’s time to look up, time to step up and not stand by. It’s time to act like it’s an emergency.
“Report after report is telling me that my future is going to be dire, and my government is telling me not to worry and pay into a pension.
“But we have a choice. We can choose to highlight that our climate is breaking down, we can choose to resist this government that is betraying us, we can choose to step up and not stand by.”