Baker held his nerve to come through the final set against the world number 189 from Chicago as he progressed through to the men’s draw at Melbourne Park.
Next up for the 26-year-old will be a first-round clash with Lukas Rosol, who famously beat Rafael Nadal at Wimbledon last year.
James Ward fell agonisingly short of sealing a place in the main draw as he lost 6-3 7-5 to Germany’s Julian Reister in the third and final round of qualifying.
British number one Andy Murray will begin his bid for a second Grand Slam title against Dutchman Robin Haase, with a potential semi-final meeting with Roger Federer on the horizon.
Laura Robson meets the 2012 Birmingham champion Melanie Oudin in the first round at Melbourne Park, while Heather Watson faces Romania’s Alexandra Cadantu.