Would upgrading my router help me with lag spikes?

I've been getting super frustrated at the fact that whenever I try playing Overwatch with my friends, my ping will be fine for like the first 60 seconds of gameplay, but then it'll spike to 4,000 ping and last for like 5 minutes, go down to normal, then may or may not continue again. I tried disabling Internet Protocol Version 6, and that worked for a little, but it's come back. I know my router's a piece of crap (link below), but we only have 20 mbps down internet and I'm not sure if getting a more expensive router would be worth it. Also, my setup is desktop pc wired to the router, and the router plugs into the wall (I live in a casita so the wall gets internet from the house)

Thoughts?

Link to router: http://www.amazon.com/TP-LINK-Wireless-300Mbps-Certified-TL-WR841N/dp/B001FWYGJS/ref=sr_1_1?s=pc&ie=UTF8&qid=1464552718&sr=1-1&keywords=router