With the match goalless late on, Arteta introduced Dowman - and the youngster quickly transformed the game.
His cross caused problems for Everton goalkeeper Jordan Pickford, allowing Viktor Gyokeres to tap in from close range. Minutes later, after Arsenal cleared an Everton corner with Pickford upfield, Dowman raced clear, beat two defenders and calmly rolled the ball into the empty net.
At 16 years and 73 days, he became the youngest scorer in Premier League history and the youngest player to score for Arsenal.
"I had a gut feeling," Arteta said in his press conference. "Yesterday he was training and I had a gut feeling that it was a moment for him, probably because he doesn't seem to be fazed by the occasion or the moment or the context or the opponent. He just plays so naturally. He makes decisions to make things happen and what he delivered was incredible."
Arteta said the teenager's influence changed the match.
"It is not only the goal that he scored," Arteta told Sky Sports. "He changed the game. Every time he got the ball, he makes things happen and we are more of a threat.
"To do it at that age, in this context, with the pressure and expectations to win the game, it's just not normal."
"It was a great moment," Arteta added. "Especially the way the goal built up. We had 10 or 15 seconds to really enjoy what was about to happen.
"It was magical, all the bench and players together jumping up with the crowd, it was a beautiful day."
Arteta also praised the youngster's fearless approach.
"It's so organic for him, he doesn't feel the pressure," he said. "He goes, gets the ball, stops on the ball.
"It's natural for him, that's the best thing, so just make sure he does what he feels. When you have such a talent then I'm sure good things are going to happen."
"For many years people that were in the stadium today will say 'I was at the Emirates when that kid at 16 scored that goal in such an important moment of the season'," he added.
Chelsea head coach Liam Rosenior has criticised referee Paul Tierney after a bizarre pre-match moment saw the official standing in the middle of the Blues' team huddle before their clash with Newcastle United.
Manchester City failed to close the gap with top of the table Arsenal after a 1-1 draw in their Premier League match against West Ham United the London Stadium on Saturday.
Arsenal struck two late goals to down Everton 2-0 and keep up their Premier League title-winning pace, as Newcastle backed up their victory over Manchester United by edging Chelsea 1-0 at Stamford Bridge.
Antoine Semenyo has enjoyed a remarkable rise at Manchester City after being crowned the Premier League Player of the Month for February, capping off an outstanding run of form in his first weeks at the club.
