You can also screw through the sides of dishwasher into cabinets. Be careful of screw length, but most dishwashers have built in spots to do this. Some behind a trim plug.

If top is only option, epoxy wood filler works great just predrill after epoxy sets. If you have dishwasher out, consider sealing the bottom of counter above dishwasher. Many dishwashers vent to the top and that may have softened the pressed wood that the screw was in.