The victory consolidated their sixth-place position, moving the north-east club on to 50 points with eight matches remaining, the same as Chelsea who are fifth with a better goal difference.
Newcastle are eight points clear of seventh-placed Liverpool, who are assured of a Europa League spot after winning the League Cup, and 10 points clear of arch-rivals Sunderland in eighth place.
Newcastle virtually wrapped up the game in the first 12 minutes with Cisse opening the scoring by side-footing home from close range after six minutes.
Ben Arfa doubled their lead after a rapid counter-attack ending with a another well-worked goal and Cisse made it 3-0 following a clever move involving a pull-back from Ben Arfa.
It was Cisse's fifth goal in six Newcastle appearances but he was later carried off on a stretcher with a suspected knee injury.
Newcastle blew a 3-0 lead against West Brom and drew 3-3 on the last day of last season so the Baggies took heart after Shane Long took advantage of a defensive mix-up to make it 3-1 after 52 minutes, but Newcastle held on for all three points.
The match was the only one played on Sunday with Manchester United and Fulham completing the round of fixtures when they meet at Old Trafford on Monday.
Manchester City, who drew 1-1 at Stoke City on Saturday, lead the standings on goal difference from United on 70 points, followed by Arsenal on 58 and Tottenham Hotspur on 55. West Brom are 14th with 36 points.
