David Moyes' men retained fourth place in the Premier League with victory - Leon Osman's deflected opener and Jagielka's excellent effort rendering Arouna Kone's late response mere consolation.
The hosts were wayward with several early attempts with Sylvain Distin the first to fail to find the target from Thomas Hitzlsperger's 11th-minute corner.
A clearer opening presented itself quickly when Leighton Baines scampered towards the by-line and cut back invitingly for Steven Pienaar - only for the South African's shot to deflect wide.
Strikers Nikica Jelavic and Victor Anichebe wasted half-chances in the air while at the other end, Ronnie Stam eventually worked home goalkeeper Tim Howard with a tame long-range drive.
The second half was a far livelier affair and Everton displayed a renewed sense of urgency from the outset - epitomised by a fantastic effort from Hitzlsperger in the 47th minute.
The Germany international neatly nutmegged the advancing James McCarthy just inside Wigan territory and pushed the ball forward before unleashing an arrowing 30-yard drive that crashed off the top of the crossbar.
Five minutes later, Goodison finally erupted - albeit to celebrate a goal reliant on fortune - when Osman's effort deflected off the under-arm of Gary Caldwell to wrong-foot Ali Al-Habsi and open the scoring.
Wigan quickly set about their search for an equaliser and were adamant they had earned a penalty on the hour-mark as Shaun Maloney bamboozled Osman in the box with a lightning step-over and went to ground.
There was little doubt that Osman had stuck his leg out late and that he had been beaten by the trick, but there appeared to be little actual contact as Maloney fell and referee Lee Mason decided the Scot's protests warranted a caution rather than a spot-kick.
Pienaar was guilty of stepping on Caldwell's leg moments later but Wigan continued to pour forward with Toffees captain Phil Neville producing a timely block to prevent Kone from levelling.
Neville was becoming the seventh player to make 500 Premier League appearances and he went on to mark the occasion with an assist 13 minutes from time - his floated cross perfectly met by Jagielka's powerful leap for a goal that seemingly buried the game.
Still Wigan would not lie down and Kone ensured a nervy final eight minutes when he held off both Distin and Jagielka to toe-poke home and halve the deficit, but Everton clung on to ensure the Latics' winless run stretched to six games.