@JosephKarp 1...c3? doesn't work because of the threatening White e-pawn. 1...c3? 2. bxc3 bxc3 3. e6! c2 4. e7! c1=Q 5. e8=Q+ Qf8 6. Qxf8+ Kxf8 7. Qe8+ Kg7 8. Re7+ Kf6 9. Qf8#

Black's best move is 1...Qxe3+!!! forcing Queen & Rook exchange and leading to the winning pawn endgame. Then take a look at the passed Black h-pawn in the open h file. So, White cannot stop two Black d and h pawns

1...Qxe3+!!, 2. Qxe3 Rd3!, 3. Qxd3 cxd3, 4. Kf3 h5!, 5. gxh5 gxh5, 6. Ke3 h4 - Black wins. I totally agreed with illyrialady. Like illyrialady said, it's "two passers do the trick".

1. ... Qxe3+ 2. Qxe3 Rd3 3. Qxd3 (3. Kf2 Rxe3 4. Kxe3 h5) 3. .. cxd3 4. Kf3
   h5 *

Two passers do the trick.

I was looking at other alternatives. I believe that 1...c3 is the solution. The idea being is that after something like 2.Qa8+, black has 2...Qf8 (to avoid a draw by repetition). 3.Qxf8+ Kxf8 4.bxc3 Rxa2 giving black an unstoppable passed pawn.

1...Qxe3+!!, 2. Qxe3 Rd3, 3. Kf2 Rxe3, 4. Kxe3 h5!, 5. gxh5 gxh5, 6. f5 h4, 7. e6 h3!, 8. Kf3 c3!, 9. bxc3 bxc3 — White cannot stop two Black c and h pawns and Black wins!!