Bring a large pot of water to a boil. Cook pasta according to package directions. Drain and transfer to a large serving bowl. Cover to keep warm.
Meanwhile, heat oil in a large saucepan over medium heat. Add garlic and cook, stirring, until it just begins to color, 2 to 3 minutes. Carefully add crushed tomatoes and saffron with soaking liquid (the mixture may splatter) and bring to a simmer. Cook, stirring frequently, until thickened slightly, about 5 minutes.
Meanwhile, bring mussels and wine to a boil in a Dutch oven (or other large pot) over high heat. Cover, reduce heat to medium and cook until the mussels open, 4 to 6 minutes. Transfer the mussels with a slotted spoon to a large bowl. (Discard any unopened mussels.)
Strain the mussel broth through a fine-mesh sieve into the tomato sauce. Stir in crushed red pepper and simmer over medium heat for 1 minute. Season with salt and pepper. Ladle about half the sauce over the pasta and toss to coat. Divide the pasta among 4 pasta bowls, top with mussels and spoon the remaining sauce over the mussels. Serve topped with parsley and lemon zest.