Cook the white rice according to package directions and set aside to keep warm.
Pat the tilapia fillets dry with a paper towel. Season both sides evenly with salt, black pepper, paprika, and garlic powder.
Heat the olive oil in a large skillet over medium-high heat. Add the tilapia fillets and sear for 3 to 4 minutes per side until they are golden brown and flake easily with a fork.
Reduce the heat to medium-low. Add the butter to the skillet and squeeze the juice from two lemon wedges over the fish. Spoon the melting lemon-butter sauce over the fillets to baste them.
Remove the skillet from the heat. Garnish the tilapia with chopped fresh parsley and serve immediately over the steamed white rice with the remaining lemon and lime wedges.