In a beta-plus decay, it's not a single neutron which is decaying into a proton, it's an *entire nucleus* decaying into a new species.
While a free proton can't decay into a neutron, beta particle, and neutrino due to energy conservation, an entire nucleus can decay to a species of lower mass by converting one of its protons into a neutron.
An isolated proton is less massive than an isolated neutron yes, but a bound state of a neutron and proton is less massive than two isolated protons.
This is due to the binding energy of the proton and neutron. Remember E = mc^2, so as the two isolated protons had more mass, they had more potential energy that the deuterium nucleus, this energy is released in a positron and neutrino that are emitted after fusion. Edit: Typo
Classical physics gives us conservation of mass and energy, but these are approximations. Einstein proposed a system in which mass and energy are interchangeable, and mass-energy is conserved. You'll notice that every element is slightly lighter than the sum of its neutrons and protons. That "mass defect"is related to the forces and energy that holds the nucleus together. To enable positron decay, the decay must release enough energy to make up for the mass that is "spontaneously" created.
The whole system must have more energy than the state it wants to decay to. In the case of a free neutron you only have the neutron's mass to work with. Once you are in a nucleus, then you are considering the mass of all of the protons and neutrons as well as the binding energy. A proton can sort of "borrow" energy to allow a decay to happen, as long as the mass of the resulting nucleus will be lower.