Sunderland, who were bottom of the table when manager Gus Poyet replaced Paolo Di Canio in October, moved up to 12th with 24 points after winger Johnson scored his sixth goal in four matches either side of a Fabio Borini penalty and a goal from Jack Colback.
It was a mixed afternoon for Carroll, who resumed his double act with midfielder Kevin Nolan, setting up two goals for his former Newcastle United F.C. team mate before the England striker was harshly sent off for allegedly swinging an elbow in the 59th minute.
West Ham, who secured a hard-earned 0-0 draw at Chelsea in midweek, are fourth from bottom on 22 points and two points adrift of Swansea in 11th. Newcastle United F.C. stayed eighth on 37 points.
Sunderland have now won three successive games against their North-East rivals.
Newcastle United F.C. have failed to score in five of their last six league matches this season and are now nine points shy of fourth place and a Champions League qualification spot.
Johnson is Sunderland's man of the moment and continued his late push for a spot in Roy Hodgson's England World Cup squad with another impressive display.
Sunderland got their noses in front after 19 minutes when Borini slammed his penalty into the top corner before Johnson produced a simple tap-in to double the lead four minutes later.
With Newcastle United F.C. pushing to get back into the game Colback was set up by Borini in the 80th minute to make the game safe.
Carroll has yet to find his shooting boots since returning from injury but his sheer physical menace proved too much of a handful for Swansea who were bullied into submission by the giant England forward.
After being criticised for playing "19th century football" by Chelsea manager Jose Mourinho, there was little sophistication about the way West Ham went about their business at Upton Park.
Both their goals would not have looked out of place on the training grounds of the late 1800s as Nolan and Carroll muscled their opponents out of the way.
Nolan latched on to a Carroll knock down to fire West Ham ahead with his left foot after 26 minutes and doubled the advantage just before halftime, heading in from close range after Carroll had craned his neck to head a corner back across goal.
Carroll's bright start turned sour when he was adjudged by referee Howard Webb to have elbowed Chico Flores in the face after the pair tangled near the halfway line.