Clean the vanity with a household cleaner to remove any dirt or oil. Use dish soap to cut through any grease. Rinse and dry thoroughly.
Prepare a two-part epoxy according to the manufacturer's instructions. Use an epoxy that cures slowly because it will expand as it dries to create a stronger bond.
Apply the epoxy to the crack using either the syringe it came with or a toothpick. Fill the crack from the bottom up, layering the epoxy if necessary.
Leave the epoxy to cure according to the package instructions.
Remove any excess adhesive with acetone nail polish remover on a cotton swab.