Ba came off the bench at half-time with Newcastle trailing to Leighton Baines’ first half goal and he made an immediate impact with the equaliser one minute into the second period.
But Everton were denied a clear goal when Victor Anichebe’s header appeared to cross the line after being pushed onto the bar by Newcastle goalkeeper Steve Harper.
David Moyes’ side, who had already had a Marouane Fellaini strike harshly ruled out for offside, were understandably furious with referee Mike Jones and his assistants, yet it seemed they would still take the points when Anichebe fired home with only two minutes remaining.
However, Ba had the last word when he bundled in his second equaliser of the night in the 90th minute.
There was more bad news for Everton as Croatia striker Nikica Jelavic hobbled off with a first half knee injury.
“We played well and we thought we had other goals in the game but for some reason or not they weren’t given,” Moyes said. “For Anichebe’s effort the linesman was looking right along the line, that’s his job and he didn’t see it.
“I thought we deserved the win, sometimes you need decisions to go your way but they didn’t go for us tonight.”
Magpies manager Alan Pardew added: “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.
“Not many teams would come back and respond in the way we did so all credit to the players.”
While the post-match discussion was all about technology and officials’ decisions, understandably the pre-match focus was on recognising Merseyside neighbours Liverpool’s fight for justice after the publication of last week’s independent report into the Hillsborough disaster.
The club’s approach was pitched perfectly as, in addition to two mascots wearing an Everton number nine shirt and a Liverpool top with the number 6 and ball boys bearing the number 96, the names of all victims of the disaster scrolled across Goodison’s television screen accompanied by the Hollies’ ‘He Ain’t Heavy…He’s My Brother’.
In an emotionally charged atmosphere, Everton made a strong start which must have made uncomfortable viewing for Pardew, watching from the stands as he served the first of a two-match touchline ban.
Jelavic had an early goal disallowed for offside but the hosts made a deserved breakthrough in the 15th minute when Baines raced onto a clever backheel from Steven Pienaar to fire past Harper.
Belgian striker Kevin Mirallas, Everton’s transfer deadline day signing, was impressing on his first league start, while Phil Jagielka shaved the post with a volley from Jelavic’s lay-off.
After Jelavic was forced off, Newcastle came into the match more and Ba equalised in the 46th minute with a low strike from Yohan Cabaye’s pass.
Fellaini had a goal ruled out for offside, a decision which was marginal at best, middway through the second half.
Then Everton’s protests reached fever pitch when Anichebe’s 78th minute header was tipped onto the crossbar by Harper and appeared to bounce down over the line before Mike Williamson cleared.
Anichebe finally did get on the scoresheet as he turned in the penalty area to fire home in the 88th minute.
That looked to have won it for Everton, but moments later Ba latched on to Shola Ameobi’s knockdown to roll a shot under Tim Howard and snatch a point.