Everton looked to have sealed all three points when Victor Anichebe turned neatly to crack a low shot past Tim Howard with two minutes left but Ba's clever finish earned a point for his team.
Everton dominated the first half and led thanks to a fine goal by England left-back Leighton Baines before Newcastle equalised just after the interval through half-time substitute Ba.
Everton climbed to seventh in the standings on seven points from four games with Newcastle two points back in 11th.
"I never set up my team to get a draw and in the second half we showed what we are all about," Newcastle manager Alan Pardew told Sky Sports.
"I was proud of the second half because we were terrific, but the first half we lacked belief and I was shocked at how we played.
"Fortunately we've got good players and not many teams would come back and respond in the way we did so all credit to the players for that. At halftime I put some belief in the team, sometimes that's all you need."
Everton went ahead in the 15th minute when Baines combined brilliantly with Steven Pienaar before drilling a firm left-foot cross shot past goalkeeper Steve Harper.
Newcastle manager Alan Pardew responded by sending on Ba and the move paid immediate dividends when the striker ran on to a beautifully weighted pass from Yohan Cabaye and struck a firm angled left-shoot shot past Tim Howard.
Pienaar was again the creative spark as Everton almost took the lead again but Marouane Fellaini was adjudged narrowly offside after clipping in the South African midfielder's clever pass.
Everton were also denied a goal after 78 minutes when Anichebe's close-range header was tipped on to the underside of the crossbar by Harper and appeared to bounce down over the line before being cleared.
Anichebe then controlled Pienaar's pass and lashed a fierce shot into the corner of the net before Ba prodded Shola Ameobi's chested flick-on past Howard in a dramatic end to the game.
"We played well, we thought we had other goals in the game but for some reason or not they weren't given," Everton manager David Moyes said.
"I thought we deserved the win, sometimes you need decisions to go your way but they didn't go for us tonight. I felt we should have taken all three points."
Chelsea lead the Premier League standings after four matches with 10 points following their 0-0 draw at Queens Park Rangers on Saturday.
Manchester United climbed to second with a 4-0 rout of Wigan Athletic and Arsenal are third after thrashing Southampton 6-1.
Champions Manchester City are fourth following a 1-1 draw at Stoke City.
