In the briefcase scene Tom Cruise isn't firing from the hip. He's firing from what's called the retention position -- gun in close indexed just at or a little below the pectoral muscle.
 I don't know if the particular drill has a name, but I've done it in a class with Louis Awerbuck. We also did it in the Intermediate Handgun class (350) at Gunsite. It's useful when engaging a close in threat.
 As to the non-dominant hand, when firing from the retention position it's important to (1) have the non-dominant hand positioned in a way that assures it can't get in front of the muzzle; and (2) have the non-dominant hand in a position from which it can easily assume its part of a two hand grip if it become possible for you to create distance and extend the gun.
 For his role in the movie, Tom Cruise trained extensively with a former member of the British SAS. The techniques he uses in the movie are "real world" as taught in some major schools. This clip
shows some of his training.
Originally Posted by Seaman
...Such a ‘fantastic shot’ that instead of dropping the 2 perps when they are further out, he takes the unbelievable risk of allowing his would-be murderers to get within arms reach...
No. The threat had the drop on the Tom Cruise character. Assuming one has the skill and confidence, it's a reasonable tactic to close distance so the the threat's gun can be deflected. And from that close in, firing from the retention position is the indicated technique.
Originally Posted by Creeper
The Mozambique Drill. ...
No. The Mozambique involve two shots to the center of mass, a quick assessment and, upon realizing the two didn't have the desired effect, firing a shot to the head. That's what Mike Rousseau did. Here, Jeff Cooper describes it (Jeff Cooper's Commentaries
, Vol. 1, No. 1, pg 1, June, 1993):
As time passes we discover that there are a good many readers who have not been to school and who are puzzled by our reference to "The Mozambique Drill."
I added The Mozambique Drill to the modern doctrine after hearing of an experience of a student of mine up in Mozambique when that country was abandoned. My friend was involved in the fighting that took place around the airport of Laurenco Marquez. At one point, Mike turned a corner was confronted by a terrorist carrying an AK47. The man was advancing toward him at a walk at a range of perhaps 10 paces. Mike, who was a good shot, came up with his P35 and planted two satisfactory hits, one on each side of the wishbone. He expected his adversary to drop, but nothing happened, and the man continued to close the range. At this point, our boy quite sensibly opted to go for the head and tried to do so, but he was a little bit upset by this time and mashed slightly on the trigger, catching the terrorist precisely between the collar bones and severing his spinal cord. This stopped the fight.
Upon analysis, it seemed to me that the pistolero should be accustomed to the idea of placing two shots amidships as fast as he can and then being prepared to change his point of aim if this achieves no results. Two shots amidships can be placed very quickly and very reliably and they will nearly always stop the fight providing a major−caliber pistol is used and the subject is not wearing body armor. However, simply chanting "two in the body, one in the head" oversimplifies matters, since it takes considerably longer to be absolutely sure of a head shot than it does to be quite sure of two shots in the thorax. The problem for the shooter is to change his pace, going just as fast as he can with his first pair, then, pausing to observe results or lack thereof, he must slow down and shoot precisely....
It appears that some of the folks here might well benefit from some serious training.