Global trends of promoting a healthy lifestyle through a balanced diet and reducing the consumption of animal products and high-fat-content foods have contributed to the creation of new mayonnaise-like products. The aim of the study was to develop a technology for low-fat mayonnaise containing 30% sunflower oil. Canned white bean aquafaba was used as a plant-based emulsifier to create an egg-free sauce. To maintain the texture and rheological properties of the food emulsion, a water-soluble polymer such as carboxymethylcellulose was used as a thickener and a pectin–xanthan mixture was used as a gelling agent. The ratio of the main ingredients of the emulsion emulsifier/stabilizer/thickener was 3:0.7:0.3 (%). The prepared emulsion-like sauce was characterized by high sedimentation stability at the level of 98%, as well as acidity equal to 0.691 g of acetic acid equivalent per 100 g sample and pH = 3.66. The volume droplet size distribution had a mean particle size of 8.4 μm and a SPAN factor of 1.7 μm, indicating typical values for these parameters of a well-homogenized mayonnaise-like emulsion. Rheological studies made it possible to classify the samples as viscoelastic systems with a pseudoplastic flow pattern and a sufficiently high yield shear stress value equal to 132 Pa as a quantitative parameter confirming the stability of the microstructure over time. Sensory analysis confirmed high scores for consistency, taste and smell of the end-product.