In a scrappy game of few chances, David Moyes and his men managed to claw their way to within three points of the lucrative fourth Champions League spot after a freezing battle with the visiting Rams.
Carving out the better of the first-half chances, Everton should have gone in at the break at least one goal to the good but the home side never looked settled against an already relegated Derby team.
Resembling an Everton side of 12 months ago, the visitors fought and chased down everything which unsettled Moyes' men, but the gulf in class was all to visible when it came to the final third of the field.
Both teams carved out a few half-chances as the snow fell over Liverpool but the best chance of the first period fell on 17 minutes.
A Leighton Baines throw-in to Osman deep inside the Derby half was given straight back to the defender, who whipped in a low driven cross to Ayegbeni Yakubu at the back post, but the top scorer could only slice over the bar from three yards.
The visitors' only threat was through the play of Hossam Ghaly in the middle of the pitch whose constant running and neat footwork stood out in a poor Derby side, but the Rams rarely got a sight on goal past a solid Everton defence.
Following a lacklustre first half, Moyes switched Osman to the middle of the park and put Manuel Fernandes on the left and the change instantly had the desired effect, with Everton attacking straight from the off.
Shots from Fernandes and Osman tested the Derby defence and the home side deservedly took the lead on 56 minutes after the pair linked up well.
A 20-yard pass from the left wing landed inch-perfect on the toe of Osman just inside the box.
The 26-year-old took the ball in his stride and calmly side-footed it past a stranded Roy Carroll in the Derby goal.
The Blues suddenly started to find some fluency and two quick-fire long range efforts once again from Fernandes and Osman could only be parried by an unsteady looking Carroll.
Derby still looked strong in the middle of the park through the pairing of captain Robbie Savage and play-maker Ghaly.
The latter carved out the best chance of the game for Jewell's men as he played a defence-splitting pass to forward Emanuel Villa just after the hour mark, but an onrushing Tim Howard saved well with his feet.
The home team piled on the pressure and good link-up play between Mikel Arteta and Phil Neville released goal-scorer Osman in the box, but his shot stung the hands of the visiting keeper who palmed past the post.
Everton struggled to find the killer second goal to guarantee all three points and the final 15 minutes saw Derby throw everything at the home side.
Efforts from Ghaly and striker Kenny Miller had Moyes on his feet before the final whistle brought relief and three points to the home side.