Well, from Phoenix, you are a GOOD eight hours from Vegas. You are a good 3 hrs from the Grand Canyon, and almost that far from Sedona.
I would do this. Rent a car to go to the Grand Canyon and Sedona. You don't need too long to do those places (you might want to drive thru Flagstaff or Prescott (my favorite)). Then, come back to Phx and turn in the car. Fly to Vegas on Southwest (if you book in advance, you can get fares for as low as $39 each way...cheap compared to renting a car and paying for gas). Then, either fly home from Vegas, or go back to Phoenix to catch your flight. You will appreciate having a couple more days in Vegas.
Have fun!!