White to move and win (it will take a few moves!)
We just saw that 21.Qxb7?? loses to 21...Qe2!
Another idea is 21.Qc4, but that just leads to a repetition of position after 21...Qd7: White could then play 22.Qc7 and Black would reply 22...Qb5: back where we started.
22.Rxe8? would be OK if we didn't have something better: 22...Rxe8 23.Rxe8+ Qxe8 24.Qxb7 wins a pawn, but Black has time to make Luft with 24...g6. The Black queen will soon counterattack, and Black has good drawing chances.
The key to this position is to realize that the Black queen is running out of squares on the a4-e8 diagonal from which it can protect e8. The White queen controls d7; the pawn on d5 attacks the c6 square. So if we can find some way to attack the other two squares we can win immediately. For example:
FANTASY POSITION (imagine White's b2 pawn was on b3)
White to play: 1.a4 wins immediately!
In this example, the Black queen has no safe square from which to guard the rook on e8.
But in our game, White has no time to play 21.b3, because Black will simply make Luft with a move like 21...g6, and there is no more back rank mate threat. If Black has time to breathe, Black will create room to breathe.
The correct move is 21.a4! Black's reply is forced, 21...Qxa4
White to play: how to drive the Black queen off the diagonal?
And now what? Here are four possibilities: