In a large pot of boiling salted water, cook pasta, stirring occasionally, until very al dente, about 2 minutes less than package directions. Reserve at least 1 cup pasta water before draining.
Meanwhile, in another large pot over medium heat, heat oil. Add tomatoes and cook, stirring occasionally, until softened and slightly darker in color, about 8 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute more. Add spinach, yeast, and basil and cook, stirring, until wilted and warmed through, about 2 minutes.
Add a splash of reserved pasta water and cook, stirring, until mixture is saucy, about 1 minute. Add sour cream and stir until combined, then add pasta. Gradually add more pasta water, stirring constantly to prevent bottom from browning, until sauce is a thick, creamy consistency.