It is possible to achieve what I wanted by using:
./mjpg_streamer -i "input_uvc.so -r 1280×1024 -d /dev/video0 -y" -o "output_http.so -p 8080 -w ./www"
...from within the mjpg_streamer's directory. It will do all the nasty work for you by displaying the stream in the browser when using the address: http://{IP-OF-THE-SERVER}:8080/ It's also light-weight enough to run on a Raspberry Pi.
Here is a good tutorial for setting it up.
Thanks for the help!