Combine 1/2 Tbsp garlic, 1/2 tsp salt, 1/2 tsp pepper, and sage in a small bowl. Remove and discard giblets and neck from chicken. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Lift wing tips up and over back; tuck under chicken. Rub garlic mixture under loosened skin. Place chicken, breast side up, on rack of a broiler pan coated with cooking spray. Place rack in broiler pan.
Combine potatoes, squash, butter, remaining 1 1/2 tsp garlic, remaining 1/2 tsp. salt, and remaining 1/4 tsp pepper. Arrange vegetable mixture around chicken. Bake at 400 degrees for 1 hour or until a thermometer inserted into meaty part of thigh registers 165 degrees. Let stand 10 minutes.