36. ♖e1 ♕xb1
37. ♖xb1 ♖c1+
38. ♗f1 ♖xb1
39. fxe3

Well, black could play
38...Nxf1 and go up a full piece, but actually I think 38...Rxb1 remains better because after

39. fxe3

39...Rc1 will win the bishop... (if white tries to defend the Bishop:

Material: N for B. Black has a battery Rc8 and Rc5. The Nc4 can expose the battery, with a double attack on Rc1, which Qb1 alone defends. The White Kg1 has 3 flight squares. Wishful thinking shows that the Black pieces can cover all of them, with a R at c1 and the N at e3. Mate threats on Kg8 take precedence over the attack by White Qb1 on the undefended Qb4.

Candidates (35…): Ne3

35…Ne3 (threatening 36…Rxc1 37.Qxc1 Rxc1+ 38.Bf1 Rxf1#)

White has no feasible defense.

(1) 36.Rc1 moves

36…Qxb1 37.Rxb1 [else, lose a Q for Ne3 at best]

37…Rc1+ 38.Bf1 [Rxc1 leads to the mate above] Rxb1 39.fxe3

Black has won the exchange (although a deeper analysis demonstrates Black can win the pinned Bf1).

(2) 36.Ra1 Rxc1+ 37.Qxc1 Rxc1+ 38.Rxc1

I'm gonna use a somewhat different format from now on: I've seen yesterday that for such an easy combination as yesterday was I still had quite a big post because I single out every move. When something is forced or obvious, I can just connect it to the first move, so I'll do that from now on. Also, I'm switching move-order: the fastest losing reply first, main line as last (so I don't have to switch back to it).

-ML-
<35....Ne3>

Is a crushing discovery exploiting the strong Black files (especially c) whilsts threatening mate if White were to take material, as the Knight covers both g2 and f1. The variations are pretty much first move reply only.

--A--
<36.Qxb4>

Loses immediately due to the strong Black Rooks. But now, Black actually needs only one as he mates on the back rank.

<36....Rxc1† 37.Qe1 Rxe1† 38.Bf1 Rxf1‡>

0-1

--B--
<36.fxe3>

Obviously loses a lot of material, but it is White's second best move to avoid mate.

<36....Rxc1† 37.Qxc1>

Without Qxc1 White would lose both Q+R for N to Rxb1, now it's only, Q for N >_>.

<37....Rxc1†>

--C--
<36.Re1>

White's most stubborn try, delaying the Knight capture, protecting the Queen and avoiding Rxc1. Still, Black has forcing replies.

<36....Qxb1 37.Rxb1 Rc1† 38.Bf1 Nxf1>

It works:

36 ♖xc5 ♕xb1+ 37 ♖c1 ♕xc1+ 38 ♗f1 ♕xf1#. or

36 ♕xb4 ♖xc1+ 37 ♗f1 ♕xf1# or

35 ...Ne3
Now white's king no longer has the f1 and g2 squares available. This is important because if white chooses to capture either the black queen or the c5 rook next turn, then black can force checkmate: a) 36. Qxb4 Rxc1+ 37. Bf1 Rxf1# or b) Rxc5 Qxb1+ and white can only throw the c5 rook and the h3 bishop in the way but again cannot stop mate.

36. fxe3
What else can white do? Black was threatening Rxc1 with the same mating idea as above. If 36. R(a)c2 then black has at least a couple of choices. One is to trade queens and then pick off the rook with ...Nxc2. Or black can play 36 ...Rxc2. Again, the same mating idea is at work, so white cannot for example capture the queen (e.g., 37. Qxb4 Rxc1+, etc..). If white plays 36. Ra1, then ...Rxc1 and again black is ahead in material after all the exchanges. That plus a passed a pawn makes white's position hopeless.

36 ...Rxc1+
37. Qxc1 Rxc1+

There's no real 'fuss': it's both intiutive and logical to go to a square that's not unattacked by a lower-valued piece. That that does not make any difference in this position is irrelevant. Actually, with Rd1 and Rf1, White just delays Black's attack, where Re1 allows a potential Rxe3 (fxe3 in the arising position would be the only move to safe White, and so it does with Rd1 and Rf1) so Black should watch out afterwards.