In these types of positions the challenge for the player with the queen is to force the opponent's king in front of the pawn, and use that tempo to bring his king closer to the pawn. Without those critical interludes in front of the pawn Black can not make progress. Guy did a beautiful job to get the win. One missed check will allow White to promote and draw. 66. Kc7 Qc4+ 67. Kb6 Qb4+ 68. Kc7 Qc5+ 69. Kd8 Qb6+ 70. Kc8 Qc6+ Here is the first check that forces White in front of his pawn. Any other king move loses the pawn outright.
71. Kb8 Ke3 72. Ka7 Qa4+ 73. Kb6 Qb4+ 74. Kc7 Qc4+ 75. Kd8 Qd5+ 76. Kc8 Qc6+ Once again Black has danced around White's king and forces him back to b8.
77. Kb8 Kd4 78. Ka7 Qa4+ 79. Kb6 Qb4+ 80. Ka7 Qa5+ Difference dance steps, but same situation for White. Back to b8 with his king.
81. Kb8 Kd5 82. Kc8 Qc5+ 83. Kd8 Qb6+ 84. Kc8 Qc6+ Once again the White king has to step in front of his pawn, giving Black the final king move he needs.
85. Kb8 Kd6 Look who has come in town to join the party! Please welcome his majesty, the black king. He's even going to let the white pawn hang around to watch the fun.
86. Ka7 Qc7 87. Ka8 Qa5+ 88. Kb8 Kc6
89. Kc8 Qc7#
A very nice ending done with precision. I wonder if I could do that with 5 seconds left on my clock?