Carreno Busta is the second Spaniard to win the event after two titles from Fernando Verdasco.
After losing the first set World No. 10, staged a steady fightback to overhaul the 76th-ranked Ebden, who stands second on the national list behind Nick Kyrgios.
Tenth seed Carreno Busta faces another Australian at Melbourne Park, playing Jason Kubler.
Carreno Busta said, “This match was tough, I had to come from a set down. But it really helped me for the Open.
“It’s the perfect preparation for the Grand Slam. I feel very comfortable on this court. We had some bad luck with the rain, now we are waiting for the Open.”