Wales pressed hard throughout the match, and had four goals ruled out for offside, before Fishlock's goal in the 105th minute found the back of the net in front of a record crowd of 15,200 in Cardiff.
"We knew they would make it difficult. The conditions didn't make it easy. The pitch was soft. We managed the game fairly well for the most part. Abi changed the game, she was excellent. She deserved the goal," Scotland captain Rachel Corsie said after the match.
The win, in front of a record crowd of 10,182 at Hampden Park, secured their place in the final play-off round for the World Cup.
The top two-ranked play-off winners will go direct to the finals, while the third-best nation will go into a 10-team inter-confederation play-off next February.