The Welshman hit breaks of 73 and 93 to head into the mid-session interval of the first-round tie in full control, but a three-frame rally from Woollaston led to another upset in Ireland.
The 25-year-old from Leicester mounted runs to 73 and 70, the latter clinching the deciding frame, to set up a last-16 encounter with Joe Perry, who ousted Stuart Bingham in the final opening round contest 4-2.
Earlier in the afternoon, Marco Fu booked his second round spot with a 4-2 success over Mark Joyce, and he will next meet John Higgins’ conqueror Ali Carter.
And Anthony McGill kept the six-frame theme going with a 4-2 win over Robert Milkins which pairs him up with Ding Junhui for a place in the quarter-finals.
The second round began later on Thursday evening as World Open champion Mark Allen beat fellow Northern Irishman Joe Swail 4-0.
Jack Lisowski, who beat Mark Selby in the first round, crashed out to Tom Ford in a 4-3 defeat.