Shades of Fred Merkle!
I'd rule one run scores, Yanks win, 3-2.
My reasoning (somewhat weirdly): An over-the-fence homer is a homer, so the hit was registered in a situation where no force play is possible.
Normally all runs would count on a walkoff homer, but since he did not complete a legitimate circuit, the home run itself cannot be entered in the books.
Thus, one run scores.
Covering all my bases (something Jeter didn't do, evidently), it might be possible that the umpire could call him out for not touching the bag. No runs, third out, game continues, fans and teammates honked-off.
The trouble with that call is that there is no ball to make the force play, although I guess they could rule him out for going out of the baseline (second, third and home being nowhere on the path to reaching first properly).
If I'm not mistaken, in order to make the play, they will have to get back to their positions, get a new ball from the home plate umpire, and go through the motions of an official appeal prior to the next pitch.
So, just try to get the home plate umpire to call for the next hitter, and risk the wrath of a rush-the-field angry Bronx mob. I'm guessing that, even if the winning run would have scored and there is no next hitter, it has to be done. You can't get the out without a/the ball.
If the next batter will not take his position in the box, the umpire can resume play anyway, calling every subsequent pitch a strike, if I recall (while dodging batteries, coins, bottles, whatever).
Possibly better to just tell Papi, "Toto, I don't think you're in Boston anymore..."