An intraocular lens (IOL) insertion apparatus including a cartridge with an IOL-receiving chamber, a handpiece into which the cartridge is loaded, and a plunger rod that extends through a lumen in the cartridge to reliably engage the IOL therein. The chamber is stepped in one section to cause the IOL positioned therein to assume a complex curve. A lip or projection on the plunger rod is aligned with the complex curve and intersects the IOL to reliably engage the IOL across its thickness. The cartridge may be a folding type with a pair of arcuate walls and extension wings joined at a living hinge. The stepped section of the chamber may coincide with the location of the hinge.