Image credit: Reuters
It is Williams's first major title victory, and the Welshman achieved it by averaging 85 in a closely-run final.
Williams beats Veenstrato claim 2019 BDO World Trophy
Ashton, meanwhile, came back from two legs down to secure her title and regain the trophy she previously won in 2015 and 2016.
Earlier, Ashton clocked a check-out of 134 against Aileen de Graaf to secure her place in the final; Williams averaged 92 in his 7-2 semi-final win against Mark McGrath.
Richard Veenstra (84.67) 6-8 (85.36) Jim Williams
Lisa Ashton (81.04) 6-2 (78.82) Anastasia Dobromyslova
Lisa Ashton beats Anastasia Dobromyslova to pick up the women's crown
Stages 19 & 21