Love this song. I remember when it first came out.
So besides the obvious of listening to the song many times to internalize the feel and figuring out the parts, for me the key to getting this song right is to use a lot of finesse and give yourself some place to go as each section builds up the energy in the groove.
The beginning is just kick and hats. Light and tasty on the hats with soft bass drum beats.
After the first section, resist the urge to add the snare as it starts again. The snare drops in after 4 bars of the second section. Don't put too much power into it.
Listen for how as the backbeat comes up and gets stronger there is a nice change up from starting out swinging on the ride and then coming back to the hats.
Practice your buzz rolls. You don't need any toms for fills in this song. It's mostly all kick, snare, hats and ride.
I would practice it adding no crashes for the driving sections that bring you to the end. It will help you concentrate on staying steady with the groove.
It's a blues song but it has just a touch of big band swing in the later sections, where there are backup vocals and horns.
Shuffle away and then swing it a little harder at the end.
You could make a little notation chart, specifying how many bars for each section and what to add as you go section to section.