The Merseysiders had to grind out victory against a well-drilled but luckless Wigan side in heavy rain at Goodison Park on Boxing Day. A deflected strike from Osman and a Phil Jagielka header gave the Toffees what proved a decisive lead, but they needed to hang on for a 2-1 win after Arouna Kone poked in a scrappy late reply.
"It is always a little more difficult at Christmas time with people's moods and the way the weather was, so it was a terrific three points to dig it out against a good Wigan side," Osman said. " Chelsea are coming here on Sunday full of form now but we are confident and hopefully we will make a good game of it."
Victor Anichebe blazed a good chance wide for Everton after just 13 seconds but Wigan went on to control large spells of the first half with little reward. Everton upped the tempo after the break and hit the bar through Thomas Hitzlsperger before Osman broke the deadlock in the 52nd minute with a shot which went in off Gary Caldwell's arm.
Osman, 31, said: "The rules say when you hit a shot and it's on target it's your goal. Obviously it did take a deflection and the keeper may well have saved it without the deflection but it's gone in and I'm happy we opened the scoring."
Osman was then involved in a controversial incident as Shaun Maloney went down under his challenge in the area, but referee Lee Mason gave no penalty - much to the visitors' anger.
Despite their positive play, the defeat represented a sixth successive game without a win for Wigan and left them 18th in the table.
Roberto Martinez said: "We need to improve on what we do. We play well but it is important we get better in both boxes.
"We can't be conceding goals in every game, even if - like the first one - you can't do much about it."