Thaw shrimp, if frozen. Peel and devein shrimp, leaving tails intact, if desired. Rinse shrimp; pat dry with paper towels. Set aside.
Trim woody ends off asparagus. Remove tips and set aside. Bias-slice the stalks into 1- to 1-1/2-inch pieces. Set aside. Cook pasta according to package directions; drain. Return pasta to pan; cover and keep warm.
Meanwhile, in a large skillet cook and stir garlic in hot oil over medium heat for 15 seconds. Add tomato and tomato paste; cook and stir for 3 minutes.
Add asparagus stalks, wine, salt, and pepper. Bring to boiling; reduce heat. Cook, uncovered, for 3 minutes. Stir in shrimp and asparagus tips. Cook, uncovered, for 2 to 3 minutes more or until shrimp turn opaque. Stir in butter until melted.
To serve, add the shrimp mixture and basil to pasta; toss gently to coat. Season to taste with salt and pepper