Everything seemed to be going swimmingly for Town as they led 1-0 at half-time but Jobi McAnuff and Scowcroft turned the game on its head after the break.
Ipswich huffed and puffed after the break, but created little to worry Gabor Kiraly in the visitors goal, although he was in the right place to clutch Jason De Vos' glancing header late on.
Town will point to Scowcroft's winner coming from a controversial free-kick after a linesman incorrectly adjudged De Vos' superb sliding challenge on sub Dougie Freedman to be a foul, but Magilton will also know his side's poor marking at the set-piece was equally costly.
The game began quietly as Nicky Forster pulled a cross just behind Jaime Peters, before Scowcroft found Clinton Morrison behind the Ipswich defence, but Shane Supple was out quickly to smother.
Richard Naylor headed a Darren Currie corner over before another Palace set-play caused Town problems, this time Morrison getting in a header from Kennedy's floated free-kick, but it was easily gathered by Supple.
Naylor nodded over from another Currie corner, this time flicked on by Bowditch before debutant Alex Bruce tested Kiraly with a daisy-cutter from 20 yards which the Hungarian calmly saved.
A minute later he was beaten as Forster nodded on Naylor's long ball, gathered the loose ball and burst beyond Mark Hudson into the Palace box before coolly sliding the ball beyond Kiraly.
Eagles boss Peter Taylor made a change at half-time the disappointing Morrison being replaced by with Freedman.
Forster shot wide from 30 yards before McAnuff levelled out of the blue on 58 minutes, seizing on a loose ball after Naylor and De Vos had challenged Scowcroft for a high ball and slotting home from a narrow angle past Supple.
That was on 58 minutes and three minutes later Scowcroft scored what proved to be the winner. Kennedy's deep free-kick was headed goalwards by Hudson, hooked off the line by Naylor, but Scowcroft was on hand to force it over the line, with the linesman confirming the goal.