Hydraulic Cement.
I've used it to patch pinholes and hairlines in basement walls/floors where the pressure is far greater than what you'd see in a sink.
Stuff is pretty cool.
Mix it and it sets up in a few minutes.
You can mix it thin to let it run into the crack and it sets rock hard.
Get at Home Depot or Lowes in small container.
Amazon.com: Dap 14086 Box Quick Plug Hydraulic Cement 5-Pound: Home Improvement