Salif Diao piled the pressure on Leeds boss Terry Venables as Liverpool extended their unbeaten start to the season.
The unrest was triggered by Diao's 65th minute goal as he took advantage of poor Leeds defence to poke the ball into the net from three yards out.
Liverpool had dominated the first half in terms of possession but it was Leeds who had the better chances. Harry Kewell hit the bar and brought a wonderful save from Jerzy Dudek with a powerful header while Djimi Traore came close to slicing the ball into his own net.
Alan Smith also came within a couple of inches of opening the scoring midway through the half when his curled shot was deflected by Sami Hyypia.
Liverpool, in contrast, had just one real opening when a weak header by Jonathan Woodgate fell to Danny Murphy just ten yards out.
The England midfielder then thumped the ball towards goal only for Woodgate to get a vital block in and deflect the shot over.
Bowyer, who turned down a move to Anfield during the summer, was involved in a bust-up with several Liverpool players two minutes into the second half.
The Leeds midfielder and Ej-Hadji Diouf had to be pulled apart by referee Steve Dunn but no action was taken against either man.
Venables brought Mark Viduka on for Smith 12 minutes into the second half in an attempt to break down the Reds' solid defence.
However, it was a blunder by Reds defender Traore that almost gave the hone side the lead. Under pressure from Kewell, Traore overhit a back-pass to Dudek and was relieved when the Polish keeper managed to nudge the ball wide at full stretch.
Diao then opened the scoring while Kewell wasted a golden chance in the 87th minute when he blazed wide from just six yards out.