Andre Villas-Boasâ€™ had looked the goods at times last week in their eventual 4-2 loss to Chelsea and it was an impressive start to todayâ€™s fixture with Bale heading home with vigour from Tom Huddlestoneâ€™s floated cross in the 15th minute.
Tottenham grabbed a second six minutes prior to the break when Dempsey scuffed home from close range after Jose Fonte had cleared Jermain Defoeâ€™s effort off the line.
Rodriguez almost equalised for the home side three minutes after his goal with a half-volley that was kept out before Spurs held on for dear life with Southampton producing a number of late chances.
In the end though, Tottenham got the points to move to fourth as Southamptonâ€™s mediocre beginning to the season continued as they sit second bottom after nine outings.
St Maryâ€™s Stadium, Southampton â€“ 31,944
Yellow cards: SOU - nil
TOT - Sandro 65â€™, Jan Vertonghen 75â€™, Jake Livermore 90+3â€™