The Reds hit straight back when Kerevi took a pass out wide and beat four defenders on the way to the line, and he scored again under the posts only minutes later, after a brilliant Anthony Fainga'a offload put the 108kg outside centre into space.
McIntyre converted from right in front, and the Reds were back within five points, trailing 27-22.
The fightback was short-lived, however, when winger Travis Ishmaiel beat Karmicheal Hunt on the outside, and ran forty metres to score in the corner.
Brummer converted to push the Bulls' lead back out, and replacement scrumhalf Piet van Zyl scored a converted try in the 71st minute to seal the win.
The Bulls had a chance after the final siren to score a sixth and bonus point try, only to overthrow the lineout and for the Reds to put the ball out of play.
Earlier, the Reds were dealt a huge blow in just the third minute, when no.8 Jake Schatz had a knee buckle badly under the weight of a tackle and was forced from the field.
-AAP