A superb Eriksen strike and a penalty from Alli secured the hosts all three points despite James Ward-Prowse's second-half strike.
Southampton failed to clear a loose ball and, as it ricocheted around the area, Steven Davis was adjudged to have brought down Dele Alli.
"He's very positive and that is good, but at the same time we need to be careful with his injury".
Spurs made the brighter start and created the first chance after only three minutes when Son Heung-Min got behind the defence to fire in a half-volley that was tipped away by Fraser Forster.
Generally Spurs do have a very good record against the Saints since they were promoted, and have only lost one game against them.
Southampton manager Claude Puel: "They [Tottenham] have a lot of wins at home, so it's a good challenge for us".
Spurs certainly needed Alli's contribution as they battled to keep on the coat-tails of runaway leaders Chelsea.
The pressure weighed particularly heavy on Vincent Janssen, who is yet to find the form that saw him finish the Eredivisie's top scorer last season with 27 goals for AZ Alkmaar.
Spurs thought they had found the key to Southampton's success when they poached Paul Mitchell and his "black box" to head up recruitment in November 2014 but they were sold a dud. In the league game prior, they hit Sunderland for four at the Stadium of Light, meaning that they come into the game in hot form when playing away.
Shane Long replaced Gabbiadini and, with both teams now without their star strikers, it was the visitors who pulled one back seven minutes into the second half. Belgium global Marouane Fellaini headed them in front after nearly half an hour's play for his first league goal of the season and Jesse Lingard scored the second just after the hour mark from 20 metres.
Kane will be sidelined for several weeks after suffering an ankle injury in last weekend's FA Cup thrashing of Millwall.
Janssen has struggled to play well for Tottenham this season and has not contributed much to the team.
Vertonghen and Tottenham will be without Kane for Sunday's visit of Southampton at White Hart Lane.
Le Tissier has chose to offer Mauricio Pochettino an ideal team talk though, suggesting that Kane's absence should give Southampton plenty of confidence.