The Irishman broke the deadlock after 70 minutes, closing Ronald Koeman's side to within a point of Manchester United and making it six games unbeaten without conceding
Shane Long's goal gave Southampton an important 1-0 win at Swansea City which sees them close to within a point of Manchester United in the race for European qualification.
The Irish striker picked up a sensational cross from James Ward-Prowse 70 minutes into the game at the Liberty Stadium, finishing with precision from close range with a header after missing a handful of chances earlier in the game.
It was just reward after the Saints had threatened Swansea's vulnerable back line all game and, while the hosts dominated the period after Long's goal, Ronald Koeman's men stood firm to hold onto the lead and extend their unbeaten run to six games, all of which have been without conceding a goal.
Both teams came into the game in good form, with Swansea unbeaten in their last four matches, but Francesco Guidolin suffered his first loss since taking over as the hosts' new head coach in January.
Swansea named the same side from their last outing, a 1-1 draw with Crystal Palace, while Koeman made four changes. Ward-Prowse and Steven Davis were among those reintroduced and Victor Wanyama dropped out, serving the first game of a five-match suspension.
The visitors had the first chance when the ball fell to Graziano Pelle after a period of head tennis but Lukasz Fabianski comfortably saved the Italy international's 20-yard volley.
Andre Ayew then tested Fraser Forster after nine minutes but the Southampton goalkeeper was equal to it, before Virgil van Dijk headed Ward-Prowse's free-kick wide at the back post.
Gylfi Sigurdsson had scored five goals in his last six Premier League appearances and he shot well off target after beating Jordy Clasie in the 23rd minute, with the Iceland international later volleying over the crossbar at the end of Swansea's best move of the first half.
In the final minute before the interval Long headed Davis's cross straight at Fabianski, the striker passing up the clearest opportunity of the opening 45 minutes.
Oriol Romeu could have scored the first goal five minutes into the second half but could only flick an excellent Ryan Bertrand cross wide of the far post.
Southampton had the ball in the net after 57 minutes but the goal was disallowed. Fabianski dropped a cross under pressure from Jose Fonte, with Pelle turning the ball in, but referee Jon Moss ruled that the goalkeeper had been fouled.
Fabianski then saved Long's shot on the turn from 20 yards as Southampton pressed for a winning goal and the stalemate was finally broken with 21 minutes remaining.
Crosses had caused problems for Swansea all game and, when Ward-Prowse whipped in another terrific centre, Long rose highest to nod home.
The hosts felt that they should have had a penalty with two minutes to go when Alberto Paloschi went down in the box but Moss was not interested, while Fabianski turned a deflected shot from substitute Charlie Austin over the crossbar as Swansea were left just three points above the drop zone.
- Goal