The present invention is directed to golf balls consisting essentially of a dual-layer core and a cover. The core includes a center having a center hardness of 50 Shore C or greater and formed from a first HNP composition, and an outer core layer having a surface hardness of 75 Shore C or greater and formed from a second HNP composition. The first HNP composition has a material hardness of 55 Shore D or less and comprises a highly neutralized ethylene/(meth)acrylic acid/alkyl (meth)acrylate copolymer. The second HNP composition has a material hardness of 45 Shore D or greater and comprises a highly neutralized ethylene/(meth)acrylic acid copolymer. The material hardness of the first HNP composition is less than the material hardness of the second HNP composition. The cover includes an inner cover layer formed from a thermoplastic composition and an outer cover layer formed from a polyurethane or polyurea composition.