Jones rose to power the ball past Tim Howard midway through the first half before Jagielka put through his own net for the second time in successive appearances with 21 minutes remaining at the Britannia Stadium on New Year's Day.
Everton enjoyed large spells of dominance as they looked to kickstart their stuttering season but spurned a number of good opportunities.
Talisman Tim Cahill, making his final appearance before departing for Asia Cup duty with Australia, went the closest when he headed wide soon after Jones' opener.
Stoke, after successive home defeats, were at their most determined and were well rewarded for a typically physical and direct display.
Everton boss David Moyes had been hoping Jagielka, who also scored an own goal against Manchester City, could shake off a thigh injury to play.
The England defender proved his fitness to replace Tony Hibbert - who also scored an own goal in the Toffees last game against West Ham - while Louis Saha was restored in attack.
That meant Cahill was no longer deployed as a lone striker but did play most of the game up front.
Saha, without a league goal in 11 months, looked determined to make the most of his recall and burst into the area inside the first minute.
He went down as Ryan Shawcross appeared to kick him in the midriff but referee Andre Marriner saw nothing untoward.
Saha sparked the next decent Everton attack with a smart turn and pass for winger Seamus Coleman but Stoke dealt with the Irishman's cross.
Cahill led another Everton charge and fed Steven Pienaar inside the box but Asmir Begovic easily claimed the South African's shot.
Stoke should have taken the lead after 10 minutes when Jones headed a long Begovic punt through to striker partner Ricardo Fuller.
The Jamaica striker headed forwards himself to beat Sylvain Distin and open up the defence but then dragged his low shot wide.
The 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 on the left and picked out Jones with a perfect cross which the former Sunderland forward powered into the net.
Everton went close to an immediate reply but Saha snatched at a difficult chance.
The visitors had a better opportunity moments later when Leighton Baines found space to cross for the unmarked Cahill but the normally lethal Australian, despite a tight angle, surprisingly headed across goal.
Marriner had a difficult decision to make when Begovic rushed out of goal and brought down Saha just outside his area but a yellow card was the verdict.
Mikel Arteta fired the resulting free-kick straight into the wall and Baines also had a shot blocked soon after.
Saha and Pienaar combined to create another opening but the latter's shot was deflected over by Higginbotham.
Everton applied more pressure at the start of the second half but Pienaar shot well wide when he mishit a volley.
Stoke continued to pose a threat and Jones released Etherington down the right but Everton got back in numbers.
Moyes attempted to freshen up his side just after the hour by removing Arteta and Neville and sending on Victor Anichebe and Leon Osman. Jermaine Beckford was on for Saha soon after.
But within moments the Toffees' task had doubled after Jagielka's stroke of misfortune.
Everton were caught as 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 towards Fuller six yards out but got his feet tangled and it bounced off his leg and past Howard.
Everton could have replied within a minute after Cahill was brought down by Shawcross but Baines curled his free-kick narrowly wide.
But Stoke finished the stronger and the visitors were given a let-off when Fuller looked to latch onto another long ball but stumbled on the edge of the area.
Dean Whitehead then volleyed over from a corner as Everton again narrowly avoided conceding a third.