Step 1: Adjust oven rack to middle position and heat oven to 450 degrees.
Step 2: Combine chili powder, paprika, salt, and pepper in bowl.
Step 3: Reserve 1 tablespoon spice mixture.
Step 4: Pat pork dry with paper towels and season with remaining spice mixture.
Step 5: Heat oil in 12-inch nonstick skillet over medium-high heat until just smoking. Cook tenderloins until browned on all sides, 5 to 7 minutes.
Step 6: Transfer pork to wire rack set inside aluminum foil–lined rimmed baking sheet. Bake until meat registers 140 degrees, 15 to 18 minutes.
Step 7: Transfer meat to a platter, tent with foil, and let rest 5 minutes.
Step 8: Combine reserved spice mixture, ketchup, vinegar, and sugar in bowl and brush over pork.
Step 9: Slice pork and serve.
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