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First-half goals from Joey Barton and Obafemi Martins secured their first victory under Joe Kinnear, who became interim manager in the wake of Kevin Keegan's resignation.
West Brom substitute Ishmael Miller pulled one back in the 65thminute, but Tony Mowbray's side could not make their pressure count.
Barton, starting his first match since his release from prison, scored from the penalty spot in the 10th minute after Shola Ameobiwas pulled down by Ryan Donk.
Martins headed home Habib Beye's cross three minutes before half-time.
The second win of the season saw Newcastle jump to 15th place on nine points, one point behind West Brom who lost the last three matches.
West Brom dominated possession after the break with neat and tidy passing, but they desperately lacked a cutting edge at crucial moments.
On Wednesday, an intriguing fixture will see second-placed Chelsea battle against adjacent Hull City while leaders Liverpool will host Portsmouth.
Bottom-placed Tottenham, under new boss Harry Redknapp moving from Portsmouth on Sunday, are visiting north London rivals Arsenal and Manchester United are at home to West Ham United.