The Toffees had fallen behind in just the second minute when Papiss Cisse opened the scoring for the Magpies but Baines scored with a thunderbolt of a free-kick to level before the break.
Second-half substitute Victor Anichebe then finished from close range on the hour mark to send David Moyes' side fifth, just four points behind Chelsea, and Baines felt it was hugely significant.
"It was a massive three points," Baines told Sky Sports after the game.
"We were off the back of a defeat and Newcastle are fighting at the moment so we knew it would be tough.
"They set off at a hard pace but we fought back."
Asked what Everton might be able to achieve this season, Baines added: "We don't know (how far we can go). We have not talked about it a lot.
"We just have to keep winning games and putting in good performances.
"If we can stay around the boys at the top as long as we can hopefully we will give ourselves something to go for at the end of the season."