Arouna Kone gave Wigan a late lifeline but it was not enough for the visitors who, despite a hard-working display, appear to be heading for another relegation fight after a sixth game passed without a win.
The visitors thought they should have had a penalty when Shaun Maloney went down in a challenge from Osman but referee Lee Mason was not convinced. Thomas Hitzlsperger hit the bar for Everton, who also had Nikica Jelavic lay off a Darron Gibson cross and Victor Anichebe flash a shot wide with just 13 seconds on the clock.
Wigan also wanted to attack and a good Jean Beausejour cross aimed at Kone was clutched by Tim Howard. The influential James McCarthy also had a powerful effort from outside the area blocked, while Leighton Baines created a chance for Everton when he supplied Steven Pienaar and Ali Al Habsi did well to turn his shot around the post.
Everton had a series of corners in quick succession and felt they should have had penalties at two of them. Anichebe first claimed he was being held back by Beausejour and then there was an appeal for handball against Maloney but referee Mason gave nothing.
The first half came to a tame end but Everton returned with renewed vigour after the break and were soon rewarded. Hitzlsperger struck a thunderous long-range effort against the bar and then Osman aimed for goal after 52 minutes, and his shot from just outside the area struck Caldwell's arm to wrong-foot the unfortunate Al Habsi.
There was controversy as Wigan tried to respond as Maloney went to ground in the area in a challenge from Osman. Latics were incensed not to be awarded a penalty and Beausejour was booked for his protest but replays suggested Maloney may have already been going down before the contact.
Everton grabbed a decisive second 13 minutes from time. Neville was on hand to receive a short corner from substitute Bryan Oviedo and marked his landmark appearance by sending in an inch-perfect cross for Jagielka, who powered in a header off the bar.
But Wigan fought on and gave themselves late hope when Kone bundled the ball in at close range after Jagielka and Baines failed to clear from a Maloney shot. The visitors applied more pressure as time ran out but were unable to find a way through stubborn Everton defending.