Blake, the tournament's eighth seed, won the fourth title of his ATP career and claimed a first prize of $57,750.
"I feel great similar to the way after New Haven going into the U.S. Open last year," Blake said. "This is two in a row for me right before a (Grand Slam event). That was my best result yet, quarterfinals and two points from the semis. So hopefully if I get the chance, I'll win those two points here in Melbourne and maybe make it further than I ever have there."
Blake was making his third career appearance in the Medibank. He ran his career record against Andreev to 3-0.
Andreev, 22, who was un-seeded, failed in a bid to win his fourth career ATP title. He took home $33,960 as the runner-up.
The Medibank International is one of several tune-ups for the Australian Open, which begins Monday in Melbourne.