A two-stage, electrically-powered injection unit for an injection molding machine includes an extruder for plasticating material, and a separate melt accumulator to receive the plasticated material. The accumulator includes an injection plunger that is slidably positioned to inject the plasticated material from the accumulator into a mold. The plunger is rotated and translated by an electrically-driven linear actuator, such as a roller screw mechanism. The plunger extends outwardly of the accumulator barrel at the commencement of an injection stroke and is peripherally supported by a bushing at the outer end of the accumulator barrel. The outwardly-extending portion of the plunger can also be supported by a movable intermediate support member to minimize lateral deflection of the plunger and enable a longer injection stroke to be employed. The injection pressure imposed upon the plasticated material can be varied from a relatively low initial injection pressure, to minimize lateral deflection of the plunger, to a relatively higher injection pressure as the length of the portion of the plunger that extends outwardly of the accumulator barrel decreases.