Controlling the region means being in a position to have a significant effect of decisions that are taken there, particularly with regard to production levels, price range (not to high, not too low), distribution (e.g., where pipelines go), etc. Nothing subtle about that.
If the invasion of Iraq proves successful, and the US obtains secure military bases in a dependent client state as presumably intended, then it will be able to enhance much further its substantial control over what happens in the region, displacing rivals (Europe, Japan, China). These are constant struggles. Europe and Japan have understood very well for half a century that the US wants to control their energy resources, and have been seeking ways around it. A complicated and contentious matter. A non-trivial consequence of the US takeover of the second largest known reserves in the world, in Iraq, is that US-based multinationals will have the inside track, not rivals, and that potential efforts to shift from dollar-based to a broader basket (including Euro-based) denomination of oil prices will be delayed, maybe aborted. That could have significant effects on the rather fragile US economy.
The concern from 50 years ago has not been India and China of course, but rather Europe and (potentially) Japan. There was always a concern that they might move towards a more independent course. The Indochina wars were in no small part motivated by concern that loss of US control over Southeast Asia might induce Japan to “accommodate” to an independent Asia, effectively reconstituting the “new order” it sought to establish by force, and that the US brought under its control during WWII. A few years after the war, the influential planner George Kennan observed that US control over energy resources gave it “veto power” over what Japan might do in the future. Concern over European moves towards independence (what was often called a “third force”) were always prominent, and a major factor in policy planning. Control over Europe’s energy resources had a similar role. All of this has intensified since the world became more “tripolar” in the past few decades, increasingly today as Northeast Asia, based on the industrial societies of Japan and South Korea with China playing an increasingly important role, has become the most dynamic economic region of the world, also holding about 1/2 of foreign exchange reserves, and largely funding US double deficits and extravagant spending. Control over the world’s energy resources becomes even more significant in that context.