How can I repair this small hole in my basement floor?
Your best bet is Hydraulic cement. There should be directions on the tin, but it boils down to clean the hole and fill it up. I'm partial to nitrile (or latex) gloves and stuffing it in by hand for something that size. The gloves because some people have skin reactions to cement; also you can throw the gloves away rather than rinsing cement down your drain. 

If you do use your fingers to pack it in you'll still want a tool to flatten off the patch. Either a paint stirrer dragged sideways or putty knife should do nicely. It's not exactly the job you need a trowel for.

It sounds like you're right about the pressure, the water should migrate to the drain. If that hole was relieving enough pressure to buckle the floor I'd expect it to be gushing like you'd struck oil.