Premier League - Ba treble sends Newcastle third
The visitors took advantage of a limp Stoke showing in the first half to build a two-goal lead, with the Senegalese striker clinical from close range and punishing the side that but for a failed medical he might have joined in January.
Stoke were much-improved in the second half, and got themselves back into the game with a quarter of an hour remaining when Jonathan Walters blasted home a penalty.
But Newcastle were awarded a spot-kick of their own five minutes later and Ba sent Asmir Begovic the wrong way to wrap up his third, and with it the match for the Magpies.
Stoke remain 11th, and begin a week of three tricky fixtures in inauspicious fashion.
Cheik Tiote missed out for Newcastle, with Danny Guthrie given the task of filling the Ivorian's boots in central midfield.
Newcastle took the lead 12 minutes in after a quiet opening to the match. It was a direct goal, with Tim Krul's long ball going straight to Leon Best, who flicked the ball on for Gabriel Obertan. The Frenchman played a delightful cross in for Ba, who simply had to make contact to beat Begovic.
And under the pressure the hosts made mistakes.
Ryan Shawcross's slip let Ba loose on the edge of the box, but Begovic rushed out immediately to clean things up.
Shawcross clearly tweaked something, because just moments later he was substituted, with Matthew Upson replacing him.
The Potters were not helped by injuries - they also lost Marc Wilson, bringing on Robert Huth before the interval, but seemed subdued despite home form which had seen them lose just one of their last 13 matches at the Britannia Stadium.
Newcastle doubled their advantage five minutes from half-time. Upson did a poor job of heading away Fabricio Coloccini's cross from deep, and the ball fell into Best's path. He scuffed his shot, but it went straight to Ba for another simple close-range finish.
Clear chances were thin on the ground after the break, but Stoke had most of the possession and pressured Newcastle with a barrage of set-pieces and Rory Delap throws from a variety of awkward angles.
Huth flashed a header over the bar from a corner on 53 minutes when he ought to have hit the target, and when Delap fired in a flat, low throw which Walters stepped over, the ball could have gone anywhere, but was eventually scrambled safe.
It needed referee Mike Dean's intervention to give Stoke their lifeline, with Ba turning villain to bring down the ineffective Peter Crouch. It was a soft incident, but a hard-struck penalty from Walters brought the crowd alive.
Stoke had come back from two goals down in the Premier League on this very date two years ago, but there was to be no repeat this time, as five minutes later the visitors were handed a soft penalty of their own.
Best did not even fall to the ground competing with Huth to reach a long throw, but Dean spotted a push and pointed to the spot.
Ba made no mistake to notch his second hat-trick of the season and continue Newcastle's best start in 15 years.