Lee Bowyer and Mark Viduka were also on target as Albion's baptism of fire after a 16-year absence from the top continued.
Having lost on the opening day of the season at Manchester United, Albion are still without a point.
But they have at least opened their goal account after substitute Lee Marshall marked his Hawthorns debut with a goal.
Albion, boosted by playing in front of their vociferous army of fans, took the game to Leeds in the opening stages.
Transfer-listed Welsh international Andy Johnson was inches away from firing Albion into a 17th minute lead when he raced on to a cross from skipper Derek McInnes.
McInnes himself went close form 25 yards as Leeds struggled to force their way into the game.
But there was always the suspicion that Leeds had the capability to step up a gear and they did just that.
Albion were given a warning of what was to come when right-back Danny Mills hit the post with an angled drive from 20 yards in the 26th minute.
Bowyer then squandered a golden chance by firing wide of an open goal after 37 minutes.
But Kewell made it third time lucky for Terry Venables' side just two minutes later after a surging run by their Australian international striker Viduka down the right wing.
He fed the ball to Mills whose cross was drilled past the unprotected Albion goalkeeper Russell Hoult by the alert Kewell.
Kewell's strike effectively ended Albion gallant challenge and their fate was sealed just eight minutes into the second half.
This time Bowyer proved to be more clinical in front of goal, collecting a pass from Kewell before seeing his right-foot drive from 18 yards fly past Hoult and into the top corner of the net.
United's domination was confirmed 20 minutes from time when Bowyer collected a mis-placed clearance from Albion defender Phil Gilchrist and fed Viduka who walked the ball around Hoult before sliding his shot from six yards into an empty net.