Tore Andre Flo and Alan Thompson scored on their home debuts for Leeds, but two goals from Kamara and another by Jonathan Greening saw Albion to their third win over the West Yorkshire side this season.
United manager Dennis Wise was sent to the stands in the last minute for shoving Kamara as the Albion striker slowly left the pitch on being substituted.
Leeds seized a third-minute lead courtesy of comic defending from Albion. Eddie Lewis easily went past Paul McShane on the left but the winger's shot was blocked.
David Healy's follow-up was cleared off the line by Curtis Davies but the ball was played back into the goalmouth where Flo marked his home debut by heading into the bottom right-hand corner.
After their encouraging start Leeds fell to pieces as Albion hit back with goals in the seventh and 19th minutes. Thompson conceded a free-kick 30 yards out, Neil Clement's free-kick was blocked by the defensive wall but Greening struck the rebound low into the net.
Kevin Phillips then picked out Greening who became a provider as he slid the ball through to Kamara. Hayden Foxe attempted a tackle but Kamara's strength took him past the defender and he tucked the ball wide of keeper Neil Sullivan.
Leeds' confidence was shattered and, after Davies swung his boot at fresh air with a third Albion goal beckoning, Kamara continued to torment the home defence.
The Senegal international's goal-bound shot was deflected for a corner but, in first-half stoppage time, Kamara pounced again.
After a smart build up on the left, the ball was played inside to Kamara who was allowed time and space to curl his 25-yard shot into the top corner.
Leeds went in at the break 3-1 down, having been totally outplayed after Flo's early goal, and it needed a desperate save from Sullivan to scramble Phillips' shot round a post on the re-start.
Wise made a double substitution replacing defender Robbie Elliott and the ineffective Robbie Blake with attackers Tresor Kandol and Ian Moore - and it had the desired effect as Leeds looked more threatening.
Albion's vulnerability away from home surfaced again when Thompson floated a splendid 22-yard free-kick into the top corner with his left foot but Healy squandered a late opportunity to equalise.