You have to keep bobbing your head to the downbeat, or just "dance" to it with your whole body. Don't stop at 0:58, no matter what. A part of the trick is to realize that the cymbal crash at 1:02 is the on the "and" right before the first beat of the very next measure where the syncopated guitar pattern starts. So, at 1:02, it goes "and 1 and 2 and 3" etc. I don't know why, but I call this a "scoop" because it feels like I'm scooping under the downbeat that immediately follows.
So, I recommend getting your whole body into it - or just your head if you feel silly getting too enthusiastic with this (although, watch some of the best drummers out there). It's hard to have good time if your body isn't moving very much while you're playing. Some guys are subtle though and most of their movement is with very small head movements that they can feel far more than you can see.
Another tip I have is: try to sing it. Literally sing the guitar part and try to do it with this drummer (you're the guitar and he's your drummer). The more and more and more you internalize it, the easier and easier and easier it will become to just play it without thinking about it. I mean, try to reach a point where you can sing the part and tap or stomp out the downbeat with your foot on the floor, or tap something with your hands (like your legs or a desk). It's all about the rhythm, so don't be concerned with the notes if you try to sing it.
So, just get into it. Internalize it. Make it yours. If you can reach a point where you can keep tapping your foot to the downbeat during this section song (establish the beat before the section comes up), then you have the ability to play it. All you have to do is keep working at it. Before you know it, you'll be able to play this drum part along with the guitar instead of only being able to play it alone.
You might even try singing this guitar part while playing just the basic 4/4 rock beat (the one he is playing until this change).
So, another thing you can do is: don't stop playing the basic 4/4 rock groove that is being demonstrated up to this change. In other words, don't play what he's playing starting at 0:58. Instead, just keep playing the basic rock beat where you have the bass drum on 1 and 3 and the snare on 2 and 4. Don't do the syncopated cymbal crash or the crescendo fill. Just keep playing the solid rock groove. Even keep your eighths going on the hi-hats and then maybe do quarter notes on the ride cymbal if you feel up to it. Eventually, you'll begin to hear it correctly and then you might even find yourself having an easier time playing the syncopated drum part instead!
One last tip: while you're listening to the song prior to this change that begins at 0:58, focus on keeping a solid 8th note pattern with your right hand and simultaneously focus on accenting the downbeats (the quarter notes, 1, 2, 3, 4). Then, when he hits the syncopated beat with the crash+bass at exactly 0:58, just keep tapping the 8ths with the accented quarters. Don't change, or stop. Keep doing it even throughout the entire syncopated section. See if you can feel it.
Try these ideas and let me know what you think!