Lichess Puzzle 82753: Can white win with a queen and two pawns vs. rook and four pawns?

Question

Lichess puzzle 82753 involves a rook and pawn endgame where white sacrifices their rook to queen a pawn. The final position is the following (with black to move):

[FEN "2Q5/6p1/1K3pkp/8/8/4p3/r5PP/8 b - - 0 44"]

I'm not convinced white can win from here; it looks like black can swap off one pair of pawns, then set up a fortress. This seems to hold on against Lichess’s version of Stockfish, but I don't think it looks especially deep. Maybe there's a winning strategy for white, though, that it didn't find.

Question: Can white win with a queen and two pawns vs. rook and four pawns?

Answer 1

It looks very difficult for white to prevent the fortress.

The obvious sequence is something like -

[FEN "2Q5/6p1/1K3pkp/8/8/4p3/r5PP/8 b - - 0 1"]

1... Rb2+ {to kick the king one square further from the action} 2. Ka5 Rxg2 3. Qe8+ Kh7 4. Qe4+ Rg6 5. h4 (5. Qf5 h5 {if Qf5 then h5 anyway} 6. Qxh5 Rh6 {when Qxh5 it leaves white struggling to save the h pawn}) h5 {and black has 3 extra pawns, albeit the e3 pawn is likely to fall soon}

Answer 2

I think it's a draw. Don't have an access to an engine right now though 1... Rxg2 2. Qe8+ Kf5 if 3.Qxe3 Rxh2 I don't see a way to win black's rook immediately. Even if black can't capture the h2 pawn it doesn't seem that difficult for him to regroup and set up a fortress. 3. Qh5+ Rg5 leads to an immediate draw.

Missed that after Kh7 black can block Qe4+ with Rg6 as given by Brian. That variation is completely drawn.