In the absence of the injured Phil Jagielka, Osman was named as captain for Sunday's home clash with Southampton - a match in which he was making his 303rd Premier League appearance for the Toffees, a new club record as he overtook David Unsworth.
Everton went on to win 2-1, moving up from fifth to fourth in the table, and they stayed there heading into 2014 after their Merseyside rivals Liverpool lost at Chelsea.
Things could hardly have gone much better for Osman - in stark contrast to his previous outing just three days earlier.
Everton suffered a surprise 1-0 defeat to rock-bottom Sunderland on Boxing Day which ended their hopes of going the whole of 2013 unbeaten at home in the league.
The visitors' 25th-minute winner came about when Osman's miscontrol of a short goal-kick allowed Ki Sung-yueng to take the ball into the area, where he was fouled by Tim Howard, resulting in a penalty being awarded and the goalkeeper being sent off.
Osman was immediately substituted for Joel Robles and Ki subsequently rifled in the spot-kick.
And when asked about his appearances record after the Southampton game, Osman said: "It feels great, and to do it on a day when we got an important victory makes it even better.
"It is just one of those things that Jags (Phil Jagielka) missed out, and I was next in line to get the armband, but it was an extra honour to wear it this time.
"As everyone knows, the last game was disappointing, especially for myself.
"So it shows how quickly things can change in football - against Southampton, I was captain of a winning team on a record-breaking day."
Everton boss Roberto Martinez - whose side are a point clear of Liverpool and five behind league leaders Arsenal at the halfway point of the season - has remained reluctant to speculate about where the Toffees might finish the campaign.
When asked about the possibility of securing Champions League qualification via a top-four berth, the manager has spoken only about trying to accumulate as many points as possible.
But while echoing those sentiments, Osman has also made it clear that, as far as he is concerned, the top four is something Everton should be very much focused on.
The 32-year-old said: "I think you have to aim for it - if you are not, you are not really setting yourself any targets. We are certainly aiming high.
"We are still up in the fight and we are aiming to try to get as many points as we can. We are ticking along nicely."
Seamus Coleman put Everton ahead against Southampton in the ninth minute, collecting the ball from Osman on the right, bursting into the box and unleashing a powerful shot into the net.
Saints substitute Gaston Ramirez equalised in the 71st minute when his strike from distance beat Robles, who should have done better in his attempt to save.
Three minutes later, Romelu Lukaku fired in the winner - his first goal in six games - by converting from James McCarthy's pass.
Everton's next match is a league trip to Stoke on New Year's Day.