I was playing Flappy Bird trying to beat my highest score. While on one run (or fly, hehe) my friend got me engaged in a conversation. When the short conversation ended I found myself thinking about something for probably 10-15 seconds, where in this time my eyes were looking at the game on my iPad, and yet my actual attention was not on the game. I was deep in thought on the topic my friend had brought up. The moment I got back to reality, I tried to re-engage myself with the game, but within a few seconds I crashed the poor bird. I had broken my record, however. It was as if another side of me took over while i was busy thinking of something else on the side. I voluntarily tried to reproduce this situation but I failed at the multitasking (as I know some will call it). This has happened while doing other things too. How is this explained, and why can it not be reproduced voluntarily.
My interpretation of this question is that you are asking about divided attention. Some (normally easy) tasks can continue to be accomplished in conditions of divided attention, and with practice you should be able to control this.
I don't know of any research confirming your suggestion that you actually got better in such conditions. You could also look at recent studies on mind-wandering (which tend to show interruptions in the main task when you are thinking about something else) or the passive/active mode in visual tasks (in which, some argue, people actually get better when they don't concentrate as hard).