As well as “zoned out” and I think there’s another, but I can’t think of it now.
In the zone seems to appear in US sports with a first cite(so far) of 1976. The article was talking about tennis and the feeling that one gets when everything about the game is going right.
To zone in on something appears(so far) in 1958. The OED suggests that it was a similar use to hone in on and home in on.
Zone defense, in US football, appears from 1927(Pop Warner).
It started in the 1976 book “Inner Tennis,” www.amazon.com/gp/aw/d/0394400437/ref=mp_s_a_2?qid=1327757167&sr=8-2
I forgot you asked about “zone out.”
So far, 1982.