Jones rose to power the ball past Tim Howard midway through the first half before Jagielka put through his own net for second time in successive appearances with 21 minutes remaining at the Britannia Stadium.
Everton enjoyed large spells of dominance as they looked to kickstart their stuttering season but spurned a number of good opportunities.
Stoke's opener came after 23 minutes as Jones diverted another long ball into the path of Matthew Etherington and raced into the area. Etherington skipped around Phil Neville and picked out Jones with a perfect cross which the former Sunderland forward powered into the net.
Everton applied more pressure at the start of the second half but Steven Pienaar shot well wide when he mishit a volley.
But within moments the Toffees' task had doubled after Jagielka's stroke of misfortune. Higginbotham sent a long free-kick into the box which Jones flicked straight up in the air, Jagielka tried to get in the way as the ball dropped but got his feet tangled and it bounced off his leg and past Howard.
Source: PA
Source: PA