The British number one, currently at 77 in the world rankings, beat 126th-ranked Uchijima 6-2 6-4 in an hour and 18 minutes in Seoul, dominating for much of the contest before surviving a fightback by her opponent.
Raducanu will next face Belgium's Yanina Wickmayer, who had earlier defeated Czech Linda Fruhvirtova 6-1 6-4.
The 19-year-old will be eager to extend her run after making a second-round exit at last week's Slovenia Open, her first tournament since the defence of her US Open title ended in round one.
After Uchijima held serve in the opening game of the match, Raducanu won the next five in a row en route to claiming the first set.
She subsequently broke Uchijima in the opener of the second and twice more again as she surged into a 5-0 lead.
Having looked entirely comfortable, the sixth seed was then broken when serving for the match, and Uchijima's response continued with three more games to take the score to 5-4.
Uchijima then had break point at 40-30 up in the 10th, only for Raducanu to produce a couple of aces before wrapping up the victory.