Swansea controlled proceedings in the first half and Gomis saw several chances go begging before Villa produced a marked improvement after the interval.
Despite Villa growing in stature in the second period, Tim Sherwood's men were unable to make the most of the opportunities that fell their way and Gomis prodded home three minutes from time after good work by Jefferson Montero.
The win sees Swansea move to within four points of their best Premier League points total – 47 – and Monk was full of praise for his team's late show.
"Overall, I think we deserved it," he said. "In the first half we were fantastic, created a few chances and maybe should have scored a couple.
"The second half was much more even, with both teams pushing and fighting, but we dealt with a confident Aston Villa team well.
"It was similar to Monday night [the 1-0 defeat to Liverpool] in that we were fantastic in the first half, but in the back of your mind you do wonder whether the missed chances will come back to bite you.
"But [Swansea's performance] typified the character and determination we have in that changing room.
"A lot of people might question what we have to play for, but we continue to fight and push.
"We did a lot of things right. There were some big performances at a tough place to come. I'm very pleased."
