Calling original function from Sinon.js Stub

You could use a closure. For example:

var obj = {
    foo: function () {
        console.log('foo');
    }
};

var stub = (function () {
    var originalFoo = obj.foo;
    return sinon.stub(obj, 'foo', function () {
        console.log('stub');
        originalFoo();
    });
}());

JSFiddle

Sinon stores a reference to the original function in the wrappedMethod property of the stub (docs were just recently added in 2020). This can be called in the fake method.

sinon.stub(Array.prototype, 'sort').callsFake(
  function () {
    console.log(`sorting array ${this}`);
    return Array.prototype.sort.wrappedMethod.apply(this, arguments);
  }
);

const array = ['C', 'A', 'B'].sort();
console.log(`sorted array is ${array}`);

<script src="https://cdnjs.cloudflare.com/ajax/libs/sinon.js/7.3.2/sinon.min.js"></script>

And so the OP's code would be:

sinon.stub(servicecore.ServiceWrapper.prototype, '_invoke').callsFake(function(method, name, body, headers, callback) {
    console.log('---- ServiceWrapper._invoke called! ----');
    return servicecore.ServiceWrapper.prototype._invoke.wrappedMethod.apply(this, arguments);
});