Victory over the Magpies took Swansea up to 13th position in the standings, and Vorm is content that their future remains in their own hands.
The 30-year-old is quoted by the South Wales Evening Post as saying: "Even though we lost to Chelsea, we still had the belief that we could win against Newcastle. We don't have to be afraid of anyone.
"The three points are huge, and scoring in the last few seconds makes them even more massive. They were big. Fulham lost, Norwich lost and West Brom lost, but we have to look at ourselves, and we know that if we win games, we will be fine.
"Newcastle was the most important win this season."
Swansea will guarantee their survival in the top flight with two wins from their final three fixtures.