If you conquer 1 battlefield and get 1 more point from oppomemt burnout

Yes — you win. The point from your opponent's Burn Out is not a Conquer (or Hold) point, so the Final Point restriction doesn't apply to it — you don't need to have scored all battlefields that turn.

One nuance: if you were at 7 when you conquered that single battlefield, the conquer itself actually makes you draw a card instead of gaining the point (Rule 471.1.b.1) since you haven't scored all battlefields. So you stay at 7, and the Burn Out point is what takes you to 8 and wins (FAQ 1303). If you were at 6, the conquer takes you to 7 and the Burn Out point to 8 — either way you win.

The win is confirmed at the next Cleanup (Rule 472) unless the opponent burns out repeatedly and you gain 2+ points from burnouts in sequence, in which case you win immediately (Rule 431.3.c).