The Polish stopper denied both Gabriel Agbonlahor and Christian Benteke in stoppage time to preserve the lead handed to the hosts by a first-half Gylfi Sigurdsson free-kick.
Fabianski's diving save to keep out Benteke's cross-goal header was particularly impressive, and Monk was thankful to his number one, who arrived at the Liberty Stadium from Arsenal on a free transfer during the close-season.
"It's what I signed him for," said Monk. "He's a very good keeper.
"It was a very good save at the end, but that's his job.
"I don't think he had too much to do throughout the game, but at the critical moment right at the end, that's what you need him for.
"The concentration level shows what a good professional he is."
After dominating the first half, Swansea had to do their fair share of defending after the interval as Villa went in search of an equaliser.
But Monk believes his players were more than deserving of maximum points in torrential rain at the Liberty Stadium.
"I don't feel fortunate at all to win the game," he added. "I thought we were the better team.
"I think we created enough chances to get that second goal and make it more comfortable.
"With respect as well, we played against a very good Aston Villa team in very difficult conditions.
"I've never seen the pitch so soft in my time here."
Swansea next face Liverpool in the Premier League on Monday.
