Mixtures of potato starch with oils (rapeseed and sunflower) were extruded. To improve the complexation of edible oils, a catalyst was added in amounts of 3 g, 6 g, and 9 g per 100 g of sample. The aim was to obtain potato starch extrudates with a high degree of complexation and edible oils during physical modification (extrusion) with the innovative use of K2CO3 as a catalyst. Selected functional properties (water solubility index and fat absorption index) and technological properties of the obtained extrudates (radial expansion index); color in the L*, a*, and b* systems, and the specific surface area was determined from the water vapor adsorption isotherm (SBET). The fat content was determined as external, internal, or bound, and complexed by amylose to assess the degree and manner of fat complexation during extrusion. Iodine-binding capacity and the complexing index were determined to confirm the formation of amylose-lipid complexes. The incorporation of edible oils resulted in a decrease in the radial expansion index and water solubility index compared to control samples. The extrudates were dark orange. Extrudates obtained at the temperature profile L: 80/80/80/60/60/50 °C, depending on the cooking oil, complexed from 48–79% of the introduced rapeseed oil and from 36–40% of the sunflower oil. The extrusion temperature profile (H: 100/100/100/75/75/60 °C) reduced the amount of bound lipid fractions. Using potassium carbonate in the extrusion of starch-lipid systems gives hope for further increasing the share of lipids in extruded mixtures.