The battle of the Belgian brothers was one of the most anticipated clashes of the tournament at Alexandra Palace after the draw was made earlier in December.
Ronny, the elder of the two by 20 years, led by a set early, and the 48-year-old should have gone 2-0 up but blew five set darts to seal his dominance.
Kim pounced to level the match, and took the third set 3-2 before routing the fourth set without loss to progress to a clash with Stoke thrower Ian White.
Ronnie Baxter, seeded 19th, was beaten by World Youth Championship finalist Ricky Evans 3-0.
Evans dominated throughout the opening set with strong scoring that included back-to-back 140s in the second leg to move into an early lead.
Baxter improved in the second set but again the scoring of Evans was too much for him to handle.
The final set was Baxter's best and, at 2-2, he looked like halving the deficit but he missed a 131 check-out before Evans coolly hit double 16 to progress.
Steve Beaton, a former world champion in the BDO in 1996, bowed out in a 3-1 loss to South African qualifier Devon Petersen.
Petersen, who earlier accounted for Mohammed Latif Sapup 4-1 in their qualifying match, dropped the first set to the 22nd seed but bounced back to oust Beaton in fine style.
The South African hit three maximums on his way to a second-round clash with either 11th seed Justin Pipe or Arron Monk.
Mervyn King, the 14th seed, obliterated American Darin Young 3-0, with the latter winning just one leg for the encounter.
King routed Young in the opening two sets, and was on the verge of winning nine consecutive legs before Young intervened.
Young should have extended the third set to a deciding leg, but a choke on the doubles saw King wrap up the set 3-1 and progress to a second-round clash with Evans.