A last minute equaliser from Paulo Wanchope earned Manchester City a 2-2 draw at Fulham, while Newcastle against Bolton ended in goalless draw at St James' Park.
An under-fire Glenn Hoddle would have been desperate for a good start, but his side were behind after just three minutes.
The goal came when James Beattie headed home a Matt Oakley corner - which was conceded after a kicking blunder by Kasey Keller.
Beattie then showed his class again with a wonderful 30-yard free kick as he curled the ball past the outstretched left hand of Keller just before half time.
On the hour it was three for Southampton as Chris Marsden combined with Graeme Le Saux who crossed into the area and in typical fashion Kevin Phillips forced Anthony Gardner into an error and the former Sunderland star helped the ball into the net.
Spurs did grab a consolation just a few minutes later when Robbie Keane found Freddie Kanoute to score from close range, but it was nowhere near enough for Spurs.
Manchester City came from behind to seal a point against Fulham.
Just eight seconds into the second half Nicolas Anelka struck his sixth goal of the season, albeit via a wicked deflection off Zat Knight.
Fulham came back strong and earned their leveller which came from Steed Malbranque on 73 minutes, he followed up after Luis Boa Morte had beaten City's offside trap.
The West London outfit then took the lead with just over ten minutes left when Louis Saha took advantage of a David Seaman mistake as he raced past the former England star before rolling the ball into an empty net.
Just when Chris Coleman's side looked set for victory, City levelled in injury time when Sun Jihai's cross was met by Costa Rican star Wanchope to head his first goal of the season.
Portsmouth's unbeaten start to the season was ended by an impressive Blackburn Rovers at Fratton Park as they went down 2-1.
Rovers first goal came on 35 minutes when a quickly taken free kick found Andy Cole on the by-line and he pulled the ball back for Lucas Neill who rifled past Shaka Hislop.
Cole then grabbed the second in archetypal fashion just before the interval as he turned Arjan De Zeeuw on the edge of the area before beating the helpless Hislop.
De Zeeuw then made amends when he headed home from close range on 60 minutes to give Pompey hope, but Rovers held on for all three points.
Liverpool secured all three points over Leicester at Anfield, but it was not easy for Gerard Houllier's men.
The Reds went ahead on 20 minutes from the penalty spot. Gerry Taggart was adjudged to have taken Vladimir Smicer down and Michael Owen stepped up to finish past Ian Walker.
Emile Heskey scored against his old club with just 15 minutes left as he managed to steal in front of Taggart and touch home El Hadji Diouf's cross.
Marcus Bent brought City back into the game in the final few minutes when he latched onto a long ball and finished clinically, but it was not enough and the home side held on for the win.
Birmingham City left it late at Elland Road, but they secured a 2-0 win over Leeds.
The first came in controversial circumstances, as Roque Junior gave away a penalty on 76 minutes for a foul on Mikael Forssell and the Brazilian was dismissed.
David Dunn's first effort was wonderfully saved by Paul Robinson, but the England shot-stopper was adjudged to have moved off his line and Robbie Savage stepped up to take the retaken effort and made no mistake.
With just six minutes left Forssell grabbed his third goal for Birmingham since moving from Chelsea, as he beat Leeds' offside trap before finishing in clinical fashion and sealing victory for Steve Bruce's men.
Aston Villa moved up five places in the table as they recorded a 2-1 win over Charton Athletic at Villa Park.
Turkish star Alpay celebrated his recall to the side by grabbing the first. Lee Hendrie's corner on 38 minutes was spilled by Dean Kiely and the Turk lashed the ball into the back of the net.
JLloyd Samuel curled in a wonderful 20-yard effort into the top corner on the hour mark to make it 2-0
Charlton brought themselves back into the game with just a few minutes left as Kevin Lisbie scored from close range, but David O'Leary's side held on for victory.
Alan Shearer missed the chance to grab his 250th top-flight goal, as Newcastle were held to a goalless draw by Bolton at St James' Park.
Click below for match summaries:
Aston Villa 2-1 Charlton
Fulham 2-2 Man City
Leeds 0-2 Birmingham
Liverpool 2-1 Leicester
Newcastle 0-0 Bolton
Portsmouth 1-2 Blackburn
Tottenham 1-3 Southampton
Click here for Premiership table
