The win moves Chelsea up to second place on 40 points, nine behind leaders Manchester City, with both sides having played 19 of their 22 league games.
Though they still have a theoretical chance of winning the league, Chelsea would need to win their remaining three games while City, who have only dropped seven points, would have to lose all of theirs.
Those slim title hopes looked set to evaporate completely against Villa as the visitors took an early lead through Chasity Grant, but three goals in an eight-minute spell from Sam Kerr, Naomi Girma and Lauren James put Chelsea back in the driving seat.
However, Chelsea's defensive flaws this season were once again exposed as Villa battled back to level thanks to two quick-fire goals from Kirsty Hanson.
Nuesken's brilliant winner in the 82nd minute finally got the home side over the line.
In the day's other games, West Ham United were held to a 1-1 draw at home by London City Lionesses, while bottom side Leicester City take on Brighton & Hove Albion later on Sunday.
On Saturday, Manchester City strengthened their grip on top spot with a resounding 3-0 derby win over Manchester United, while Arsenal put themselves in a strong position in the race for second place by beating Tottenham Hotspur 5-2.