Whitlock, the runner-up 13 years ago, battled to a 3-2 victory over Christian Perez of the Philippines at Alexandra Palace.
Perez twice fought back from a set down and had chances in the decider but missed nine darts at double with the final set tied at 1-1.
"That was a real battle, Christian played really well and it could've gone either way," Whitlock said on pdc.tv. "I think I stayed calm, used my experience and just got lucky really."
Four-time women's world champion Ashton was bidding for her first victory on her fourth appearance on darts' biggest stage and threatened a sensational comeback against Ryan Meikle.
But, having recovered from 2-0 down to level the match, Ashton was unable to maintain her momentum in the decider as Meikle claimed a 3-2 victory.
Daryl Gurney became the first seeded player to go out of the tournament, losing 3-0 to Alan Soutar in the second round, while Adam Gawlas defeated Richie Burnett 3-2 and Martin Lukeman was a 3-0 winner over Nobuhiro Yamamoto.
In the evening session, Scot Cameron Menzies held his nerve to see off Brazilian Diogo Portela 3-1.
Dimitri van den Bergh defeated former World Masters semifinalist Lourence Ilagan 3-0 and debutant Josh Rock went 3-1 over Jose Justicia.