Martin O'Neill's Ireland dropped two points behind Serbia, who they host in Dublin on Tuesday, while Austria's prospects now appear all but doomed ahead of the visit of Georgia.
However, it took until late in the game for the Welsh to break the deadlock against a stubborn Moldovan side.
Ramsey's deflected strike in injury-time made the result safe, but in truth it was a tougher night for Chris Coleman's side than they would have liked.
The young Liverpool forward did not get his name on the scoresheet this time but did manage to provide the cross for Robson-Kanu to score the all-important breakthrough goal in the 80th minute. They dug in against Austria and the youngster Ben Woodburn did fantastically well to secure them the win. In fact it was Wales who should have comfortable put the game to bed, Robson-Kanu selfishly blasting over when Bale was free and unmarked, before hitting the post with another effort, and Bale was denied as his outrageous overhead kick was saved by Lindner.
"We have to do the same again in Moldova (on Tuesday)".
Gareth Bale has said that he helped persuade Ben Woodburn to reject the overtures of England.
Ramsey's 93rd-minute goal, meanwhile, brings to an end an excellent week for Wales, as they head into their penultimate qualifier against Georgia next month full of confidence.
The message from Chris Coleman to his players at half time would surely have been for them to remain patient, and try to move the ball slightly quicker, and ultimately it paid off. The win in Dublin leaves the Serbs four points clear at the top of the World Cup qualifying group, but Wales have given themselves an excellent chance of reaching Russian Federation via the play-offs. Top spot isn't out of the question, but with Serbia requiring a win from their last two games it's likely to be the play-offs should Wales do what they need to.
Woodburn is nevertheless unlikely to start on the bench when Wales face Moldova.
Woodburn has certainly shown a lot of promised and has been touted as a possible superstar for the future.
Woodburn was born in England but qualifies for Wales through his Swansea-born grandfather.