Oriol Romeu came off the bench to earn a point for Saints as Koeman's men cancelled out Joleon Lescott's first half opener.
The Villa captain scored just before the break in a half that Saints dominated with a number of chances. Lescott poked the ball past Maarten Stekelenburg at the back post from a corner.
Romeu equalised for Saints when the substitute scored his first for the club by turning in a James Ward-Prowse corner with a half-volley.
Saints came into the came eager to put a run of three defeats in all competitions behind them. They started the game excellently and Villa couldn't handle the early Saints onslaught. Ryan Bertrand and Dusan Tadic combined well down the left hand side on numerous occasions with Villa looking vulnerable on the wings.
Saints had a number of good chances early on with Tadic and Graziano Pelle putting the ball over the bar within the first few minutes. Victor Wanyama then headed wide from a Tadic corner before the Serbian forward found Sadio Mane who volleyed over.
The returning Jose Fonte almost found the back of the net as the captain pounced on Brad Guzan's fumble but his low effort was cleared off the line.
A minute before half time, Lescott provided a bitter blow for Southampton as the centre back managed to poke the ball in at the back post from a Jordan Veretout corner.
Just after the hour mark, Koeman introduced Juanmi and Romeu who both had a big influence on the game. Juanmi went close but couldn't quite get his head to Cedric's wonderful cross and went even closer a couple of minutes later when he was played in by Steven Davis. The summer signing played the ball past Jores Okore but his low, powerful shot was saved by Guzan,
Saints' equaliser came in the 73rd minute when Ward-Prowse's inswinging corner found Romeu at the back post who showed great desire to get to the ball and finish well from close range.
Saints pushed for a winner late on but were unable to find the back of the net. Virgil Van Dijk headed over from a corner and Shane Long shot from distance but it was Romeu's goal who gave Southampton a first win since their 1-0 victory at Sunderland on November 7th.