The scoring was opened in just the eighth minute when West Brom's Jerome Thomas brought down Luis Suarez down on the edge of the area as he went to turn and even though referee Lee Mason did not pick it up, his assistant Gary Beswick did and awarded a penalty to the visitors.
Liverpool were unlucky not to get another penalty following the earlier decision when Baggies centre-half Jonas Olsson clattered into the back of Carroll but it did not matter too much as the British record signing made it 2-0 on the stroke of half-time.
Suarez played a first-time ball into the path of Carroll with the Baggies defence all at sea and the big man took a heavy touch with his right foot before finishing just in time from an advancing Foster to make it 2-0.
West Brom at times looked like they were not interested as they were unable to provide any attacking play at all which must have been frustrating Roy Hodgson who would have been looking for a much better showing against his former club.
The Reds could have gone further ahead when Carroll forced a top save from Foster with a brilliant volley after a neat first touch from Suarez' knockdown in the 69th minute before Stewart Downing struck the upright very late - the tenth time that had occurred for the Reds this term - but it did not change the outcome of the game as the Anfield club went straight back to fifth on the table after Arsenal temporarily pushed them out of that position.
West Brom's loss forced them down to 13th and they have now beaten Liverpool just once in their past 20 meetings.
TRIBAL ASKS: If Liverpool want to be a serious contender should they winning games likes this by a bigger margin or is the scoreline irrelevant as long as they are winning?
Yellow cards:WBA - Jonas Olsson 35' LIV - nil