Villa, though, remain only four points above the drop zone after a sixth successive game without victory.
Below, Sports Mole analyses whether the result was reflective of the action at the Liberty Stadium.
On target: 8
On target: 3
Was the result fair?
The scoreline perhaps flatters Swansea, as they were not three goals better than a Villa team who matched them in most areas during the first 60 minutes. A handful of poor defensive mistakes hampered them, though, and proved costly when Shelvey and company produced moments of class to punish them. A deserved victory for the Swans, who recorded back-to-back wins for the first time since 2012.
The fact that they had less possession at home than a Villa side who are known for being counter-attack specialists indicates that Swansea's passing game was nowhere near its best. What they did very well, though, was defend, particularly Ashley Williams, who headed away several good crosses and made a couple of crucial blocks. The obvious highlight was Shelvey's goal, which required great confidence as well as execution, but was only a part of the midfielder's excellent overall display. Bony showed again that he is a clinical finisher, and Hernandez's strike completes a quartet of well-taken goals.
Focusing on a player that was not playing for a minute, Christian Benteke was an obvious miss up front as, despite scoring, Agbonlahor could not make the most of what was often very good delivery into the Swansea box. Ashley Westwood had a good game, helping Villa largely control a midfield which is used to having the majority of the ball, particularly on home soil. Fabian Delph played his part too, and Roy Hodgson could do a lot worse than look at the 24-year-old if injuries disrupt his current plans for England's World Cup midfield. They were a mess at the back, though, with large gaps between the centre-backs being exploited for two of the four Swansea goals. Poor marking also assisted Hernandez's effort, and Paul Lambert's men will have to tighten up if they are to be sure of survival.
Sports Mole's man of the match
Jonjo Shelvey: His once-in-a-lifetime goal would be enough for him to win this award, considering that it also came at a decisive point in the game, but Shelvey's contribution was not limited to that. He also supplied Bony's opener with a measured through pass, tested Guzan from distance on a couple of other occasions, and was a combative and yet composed presence in the centre of midfield. A very good performance, capped by one moment of magic, which is certainly a goal of the season contender.
Although Shelvey had everything to do when Baker's clearance fell to him for Swansea's second goal, the midfielder would never have been given the chance to pull off the spectacular without the Villa defender's miskick. Guzan was blameless because of the precision and skill of the strike that followed.
A penalty call at each end were the only notable decisions that Mark Clattenburg had to make, and he got both of them spot on. Bony went to the ground far too easily under the challenge of Baker, whose blatant barge of Marvin Emnes in the other box did not need a great deal of consideration from Clattenburg. He should also be applauded for sensibly managing a couple of tussles in a feisty finish to the contest.
Swansea: Monk will be hoping for two more victories to further stake his claim for the permanent managerial vacancy, starting against Southampton in their final home game of the season.
Villa: Lambert will feel that points at home to Hull City next weekend are a must if they are to be sure of safety, as they finish their season with trips to Manchester City and Tottenham Hotspur.