Heat a skillet over medium heat. Add onion, celery, garlic, salt, and pepper. Cook and stir until slightly softened, about 3 minutes. Add diced tomatoes, vodka, lemon juice, hot sauce, and Worcestershire sauce. Bring to a simmer. Cook until sauce is hot and flavors are combined, about 5 minutes.
Fill blender halfway with sauce. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend. Pour into a lidded jar or container. Repeat with remaining sauce.