The England left-back levelled for the Toffees with a sublime 43rd-minute free-kick to cancel out Papiss Cisse's second-minute opener before substitute Victor Anichebe produced a winner on the hour-mark.
The victory allowed Everton to move to fifth on the table and it was a result very much welcomed by Baines who believes anything is possible at Goodison Park this season.
"It was a massive three points," Baines told Sky Sports.
"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."
He 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."