Adebayor, whose best efforts could not lead his country to the African Nations Cup, took his tally for the season to 19 with a bullet header late in the first half.
It was a ninth strike in his last seven appearances - scoring in each and netting the opener in three successive league matches.
A superb 25-yard goal by Mathieu Flamini midway through the second half and another from Cesc Fabregas made sure of a 11th home win for Arsene Wenger's men, who leapfrog over Manchester United, for 24 hours at least.
Wenger believes Adebayor has come a long way in a short time since arriving from Monaco in January 2006.
"He has many assets for a striker - he is mobile, he is tall and has quick feet," said the Arsenal boss.
"He can score with his feet, in the air, on crosses with headers. He is a generous type of player, he works for the team.
"He is striker who you dream to have."
Wenger was pleased with the efforts of his side, who have shown few ill effects from the Carling Cup semi-final defeat at Tottenham last week.
He said: "Maybe both sides were a little bit less sharp physically than the first game on Saturday, but overall we controlled the game.
"We knew when to hold the ball and to accelerate.
"We could have scored more, but Newcastle worked very hard and it was important for us not to make a defensive mistake."
Wenger added: "For us, it is good to win tonight and see what they (Manchester United) will do tomorrow.
"It is too far to go to just concede at every single result.
"What's important for us is to be level with United and Chelsea going into April, so we need to be consistent and win our games."
Wenger added: "They can dig in and I feel we are much more mature than last season.
"We can be patient, move the ball and keep our concentration, not making a mistake. Last year, we were not capable of doing that."