Reading seemed on course for their first Premier League win of the season after goals from Jimmy Kebe and Noel Hunt in the space of four second-half minutes.
Ba had equalised in between the two Reading strikes with a magnificent volley but his contribution then veered from the sublime to the ridiculous.
The Senegal striker went to meet Shane Ferguson's cross with his head but missed it and the ball deflected off his hand past the helpless Reading goalkeeper Alex McCarthy.
Reading then threw everything they had Newcastle in vain search of the winner but Jason Roberts was denied by an excellent save from Steve Harper before Jobi McAnuff hit the post.
In the end the Royals had to settle for a point, which was not quite what their supporters had hoped for on Alan Pardew's return to the Madejski Stadium.
The Reading faithful have not forgotten how Pardew, having laid the foundations for the club's current success, resigned as manager in 2003 so he could take charge of West Ham.
Newcastle took the bold step on Thursday of handing Pardew a contract which runs until 2020.
And each time Reading took the lead, the home support took great delight in warning Newcastle fans: "Eight years for Pardew? You're having a laugh".
Both Reading goals were set up by club captain McAnuff, who returned to the side after missing the Capital One Cup victory over QPR.
Pardew, whose touchline ban expired on Saturday, gave a first league start to Gael Bigirimana alongside Cheik Tiote in the centre of midfield, with Vurnon Anita dropped to the bench.
Bigirimana immediately looked at home in the centre of midfield, dovetailing nicely with Tiote as Newcastle controlled the middle of the park.
But they could not create anything from that platform with Hatem Ben Arfa a passenger for most of the game while Ba was erratic and Papiss Cisse anonymous.
Reading grew into the game and had the best chance of the first half when Pavel Pogrebnyak's header, after a patient build-up, was palmed over by Steve Harper.
But otherwise there was little to get the fans of either side excited.
It took 24 minutes for the first shot on goal, which fell to the left-back Nicky Shorey and his volley went out for a throw-in, which pretty much summed up the quality of football on show.
Pogrebnyak then found himself a yard of space in the Newcastle box but the ball bounced awkwardly and he shinned it over the bar into the crowd.
Reading worked the ball wide for McAnuff, who curled an inviting cross in for Pogrebnyak to meet above Taylor at the far post but Harper launched himself well to tip his header over the bar.
James Perch was booked for a foul on McAnuff but then provided vital intervention as Pogrebnyak was readying to shoot, after chesting the ball down in the box.
Pogrebnyak continued to cause problems after the restart, getting the better of Taylor to break into the box but his control was poor and Michael Williamson cleared.
Cisse's low shot was blocked by Kaspars Gorkss - and suddenly the game awoke from its slumbers with three goals in four minutes.
Kebe put Reading ahead. The Mali striker was played in by McAnuff and ran at Perch, who got himself in a tangle and Kebe scuffed a low shot inside the near post.
Newcastle hit back within seconds and it was no surprise that Tiote was the creator, clipping the ball towards Ba who met it with spectacular volley on the run.
With barely a chance to draw breath, McAnuff then worked his way to the byline and whipped in a cross which Hunt met with a precise, glancing header to beat Harper at his far post.
The chants aimed at Pardew resumed - but they were quietened just six minutes from time in controversial fashion when Ba stooped to meet Ferguson's cross but handled it into the net.
Reading upped the ante and Roberts, on as substitute, forced another top save from Harper with a strike from distance and McAnuff saw a shot rebound back off the post.
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