Sorry about not getting back to this topic, I've been trying to figure out if there is indeed a problem here or if I'm just overly paranoid (which is a definite possibility!).

So far I've run a full scan with Malwarebytes, and both a boot-time scan and a full scan with Avast. Neither have come up with anything.
I noticed this happened on the 8th at around 2am. I was browsing using Chrome on a trusted forum when I saw hard drive access and decided to check out my current active connections in Comodo. Like I said, there were dozens (over 100, easily) of outgoing connections from my PC to my router on port 4444. I think the source ports were all different. But the latest Chrome version seems to have been downloaded and updated at exactly the same time this happened, so I'm wondering if maybe it's a Google Updater oddity?
There's absolutely nothing online about this, so I'm concerned. One post I found alludes to port 4444 being used for IPv6, but I don't see why over 100 connections would need to be opened to the router...
If I remember correctly, Comodo was reporting that all the connections were 66 bytes long, both in and out. I'm not sure, I think the process opening the connections was svchost. I should have taken a screenshot!
I haven't seen any odd connections since then, though. Nothing connecting to the router on 4444, no ports listening, nothing out of the ordinary. I'm still worried, though...
There are multiple PCs on my network, one of which was online at the same time this happened.