O'Sullivan, 41, chasing a fifth Welsh Open title, recovered from going a frame down to beat Tom Ford 4-1 and set up a meeting with Mark Davis.
Fellow Englishman Selby, 33, did not drop a frame as he beat Liam Highfield.
Wales' two-time world champion Mark Williams suffered a surprise 4-3 defeat by world number 115 Elliot Slessor.
There was another surprise exit as China's world number five Ding Junhui was knocked out in the first round in a 4-2 loss to Finland's Robin Hull.
World number four Judd Trump eased through 4-1 against Andrew Higginson, while Scottish Open champion Marco Fu beat Martin Gould 4-2.
Fifteen-year-old Welsh schoolboy Jackson Page is back in action on Wednesday, when he faces John Astley in the second round.
The teenage wildcard entry eliminated world number 123 Jason Weston in the first round of his debut professional tournament on Monday.
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Defending champion Ronnie O'Sullivan and world number one Mark Selby both progressed to the second round of the Welsh Open on Tuesday.