The 18-year-old, who is the reigning junior doubles champion at both the US and French Open, saw off France's Kenny De Schepper 6-4 6-4 at Devonshire Park.
Edmund, from Beverley in East Yorkshire, played his first main tour match at Queen's Club last week and was hugely impressive, serving out to love for a win over a player ranked 360 places higher.
In the second round Edmund, who has a wild card into the main draw at Wimbledon, is due to face second seed Gilles Simon, who hobbled off the practice court on Monday with ice around his left ankle.
"It's nice to have this win," said Edmund. "I had the intent of trying to put a lot of balls in play and go from there. It worked out great. I'm just happy to get the win after being given a wild card and this great opportunity. It's a nice feeling."
Sixth seed Alexandr Dolgopolov lost to Fernando Verdasco despite dominating the first set, the Spaniard winning 1-6 6-3 6-2.
Former champion Andreas Seppi survived a stern test against qualifier Guillaume Rufin and eighth seed Fabio Fognini also won but there were mixed fortunes for American qualifiers James Blake and Ryan Harrison.
Harrison prevailed in a final-set tie-break to defeat Paul-Henri Mathieu but Blake was beaten in straight sets by Spain's Albert Ramos.