Lambert spurned two glorious chances in the opening minutes from close range.
Both sides hit the woodwork in the first half with Shane Long’s header striking the post while Jay Rodriguez rattled the bar with a long-range effort.
After Fonte had broken the deadlock from close range, Jack Cork’s long-range effort hit the bar in the dying minutes.
The result leaves Steve Bruce’s men in 13th place while the Saints move up to eighth.
4' –LAMBERT CHANCE - The striker should have scored! He hammered the ball from 12 yards out but it curls inches wide.
7’ – LAMBERT AGAIN - Lambert is put through on goal and tried to lift the ball over the keeper but Harper is equal to it.
11’ – INJURY - Paul McShane is carried off on a stretcher with an injury to his left ankle.
13’ – WOODWORK - Long hits the post with a glancing header from Elmohamady's cross.
30’ – RODRIGUEZ GOES CLOSE - The striker hits the bar with a curling effort from 25 yards.
40’ – CHANCE- Jelavic’s toe-poke from the edge of the box is fired at straight at Boruc.
45’+6 – CHANCE - Rodriguez heads over at the back post from Lallana's cross.
57’ – DOUBLE CHANCE - Davis feeds Lambert, whose low shot from a tight angle is saved by Harper. Rodriguez then shoots straight at Harper but is flagged off-side.
69’ – GOAL! Hull 0-1 Southampton - Fonte hacks the ball in despite Hull's clearance hack off the line. Lambert knocks in the rebound to make sure.
86’ – SAINTS GO CLOSE - Shaw's low shot is parried by Harper with Guly's rebound cleared off the line by Davies.
88’ – CHANCE - Jelavic runs onto Aluko's through ball but spoons his effort over the bar.
90’ – ALUKO MAGIC - Aluko's long-range effort is parried by Boruc diving to his right after a neat bit of skill.
90’+1 – WOODWORK - Cork rattles the bar with a long-range effort.
Hull have conceded 10 league goals at home this season, only one more than Chelsea, Man City and Liverpool.
The Tigers had just 33 per cent of the possession.
Southampton now have 39 points, their joint-highest ever in the Premier League at this stage of the season.
Jose Fonte has scored three goals this season.
TALKING POINT: Did Rickie Lambert or Jay Rodriguez improve their chances of being picked for the World Cup? Lambert missed two gilt-edged chances in the first half, before testing Steve Harper with a low shot after the break. Rodriguez, with seven goals in his last eight away games, always looked a threat and looks the more likely to be Roy Hodgson’s wild card pick. He hit the bar with a brilliant whipped effort and went close with a header.
MAN OF THE MATCH
Curtis Davies (Hull City): The centre-back made a superb clearance off the line, his positioning was good and he was solid in the air. If he steers clear of injury, he will be pivotal to the Tigers' hopes of survival.
Hull City: Harper 6, McShane 5, Davies 8, Bruce 5, Figueroa 5, Livermore 5, Huddlestone 6, Elmohamady 7, Meyler 6, Jelavic 6, Long 6. Subs: Brady 5, Boyd 6, Aluko 6.
Southampton: Boruc 5, Chambers 6, Fonte 7, Yoshida 5, Shaw 6, Cork 6, Schneiderlin 5, Rodriguez 6, Davis 6, Lallana 6, Lambert 5. Subs: Wanyama 4, Ward-Prowse 4, Guly 5.
MATCH IN A TWEET