Question about graphics and ping

Hello, not entirely sure where to put this. This seemed to be my main area of interest though.
I was wondering if having a lower end GPU would have any effect on my ping in games. If not, could this maybe be another problem? I'm running an i5 3570k with the intel 4000 and every game(guild wars, tf2, dota2, other steam games) I play has some sort of stuttering issue. I've been pinging google during these times and I often get large spikes at random intervals. They range from around 300-2000. Shorter=shorter stutter, etc. I'm running on wireless, but i've also tested the stick on another computer with no issues at all. The computer did have an actual GPU and not an integrated. I've always thought that latency had no connection to graphics cards, but maybe i'm wrong. I've tried to research on this, but haven't been able to find anything that's useful. Thanks.

Edit: I've tested out the stutter and i'm certain that it's not my router. I've had two computers side by side pinging google when the stutter appears and only the one that i'm running the intel 4000 on has the problem. They are both running wireless, so i'm not sure if that's a factor.
Also, when the stutter happens, there's no dip in fps. I'm not really sure what the problem is. I've got updated drivers, so drivers don't seem to be the problem. The problem popped up a few days ago. I'd been running the computer fine for a good week before this problem popped up. I didn't download anything, so i'm a bit confused as to what is causing this.