Muller, ranked 44th in the world, slammed down 22 aces to 21 by the towering Karlovic, who holds the world record for career aces, for a narrow 7-6 (7/5), 7-6 (7/4) win at the grasscourt tournament in the Netherlands.
Muller will bid for his first career trophy on Sunday against either French title-holder Nicolas Mahut, ranked 49, or American Sam Querrey (37).
CoCo Vandeweghe eased into the women's final, beating fellow American Madison Brengle 6-4, 6-2.
Vandeweghe, ranked 43rd, will bid Sunday for a second title in the event, after 2014, when she plays France's Kristina Mladenovic.
The 32-ranked Mladenovic defeated Swiss top seed and close friend Belinda Bencic 2-6, 6-3, 6-4.