You know, how if you kill an Elite around a Grunt they may panic? The way I look at this, is Elites are like the big brothers to the Grunts.
Use that to an advantage: Don't always go in shooting. If a room has grunts in it, chances are they might be asleep. Good example is the Assault on the Control Room; my reasoning is that they feel safe in a "secure" area.
Sneak around and gun-whip patrolling covenant in the back before they can shoot at you; as long as no shots are fired, the grunts stay asleep. When all the patrolling enemies are dead, simply proceed in a big game of whack-a-grunt. This is most useful I think in an inside room about halfway through AotCR where there are about 25 sleeping grunts with only 2 patrolling elites.