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Selby recorded five breaks of 50 or more with one century of 119 in his opening-round victory, which featured a handful of hard-fought frames after some questionable misses and shot choices.
Qualifier Brown, ranked 74 and into his first main draw at the Crucible, twice led Selby in the early stages, but ended the first session trailing 5-4.
Selby then extended his lead on Tuesday afternoon to 7-4, only to see Northern Irishman Brown fight back and reduce the deficit to one frame.
However, the comeback stopped there as Selby booked a second-round meeting with Noppon Saengkham.
Shaun Murphy became the third seeded player to leave the World Snooker Championship on Thursday after he was defeated by Noppon Saengkham in the first round.
Resuming the match trailing by three from the first session – at 6-3 down – Murphy again struggled for fluency, failing to construct a run in excess of 50, winning just one of the five frames played. The world number 42 Saengkham produced runs of 53, 63, 52, 50, 60 and 76 in an excellent morning session of snooker to seal progress to the second round.
The victory means Saengkham becomes just the third Thai player to register a win at the Crucible after Dechawat Poomjaeng and James Wattana, while Murphy joins David Gilbert and Jack Lisowski as seeded players to exit the tournament at the first-round stage.
Saengkham, who also compiled runs of 64, 67 and 59 in a standout showing, will play Mark Selby or Jordan Brown in the next round.
Also in the morning session, debutante Jamie Clarke put Mark Allen through his paces to end the session trailing by just one frame, 5-4.
After Allen opened with two centuries, Clarke, who is currently ranked 89th and the lowest in the tournament, responded with a third to show real intent.
The winner will play Anthony McGill in the second round.