Bristol City's 2-0 win at Fulham put the Robins right in the promotion picture, while leaders Leeds United beat Huddersfield Town.
Manchester City have a favourable draw in the FA Cup third round, but there are difficult trips for Everton and Manchester United.
Leeds United claimed a late win over Reading to move top of the Championship as Michael O'Neill suffered his first loss as Stoke City boss.
Preston's loss to Derby gave West Brom and Leeds the opportunity to boost their positions in the race for promotion from the Championship.
Three players have left the Scotland squad, including Scott McTominay and Andrew Robertson.
Jake Livermore was on target as West Brom saw off Hull City, while there were wins for Preston North End and Leeds United.
Leeds United picked up a first win in three at home to QPR, sending them above Swansea City to the Championship summit.
Derby have sacked Richard Keogh, who sustained a season-ending injury in a car crash the club described as an "alcohol-related incident".
Hal Robson-Kanu looked like he had extended 10-man West Brom's lead in the Championship but Charlton stole a point.
Lee Johnson's Bristol City left it late but claimed all three points against Charlton Athletic, while Fulham beat Luton Town 3-2.