Back-to-back wins under new manager Paolo Di Canio have lifted the Wearside outfit to six points clear of the relegation zone, although Wigan have a game in hand on the cluster of teams above them.
And Vaughan, who scored a stunning goal in the memorable 3-0 derby victory over Newcastle at St James' Park, feels another three-point haul against 17th-placed Villa will be enough to ensure that the relegation fears which led to Martin O'Neill's departure can be banished.
He told The Chronicle said: "Do I think one more win will keep us up? Yes, I think it almost certainly will.
"If we beat Aston Villa on Monday there will be a six-point gap between us, there will be a gap between us and Wigan and maybe one or two others.
"So reaching 40 points will be significant if we can do it. It will make it difficult for other teams to catch us with games running out - especially as our goal difference is good compared to a lot of other teams."
Despite Villa's perilous position in the table, Wales international Vaughan is expecting a tough encounter against Paul Lambert's men, but he insists Sunderland will head to Villa Park full of confidence.
He added: "It is going to be a very difficult game but it feels like we have momentum after our last two wins.
"You can feel how the mood has changed inside and outside the club on the back of those wins. The belief and confidence in the squad has improved in the last few weeks.
"We can see the things we are doing on the training pitch are working, so we have a belief in the system and want to keep it going."