Goals from Christian Eriksen and Dele Alli in each half extended Tottenham's unbeaten home record as they claimed a 10th successive league win at White Hart Lane.
Questions had been asked about how Tottenham would cope without injured striker Harry Kane but they were answered after 14 minutes when Mousa Dembele found Eriksen and the Dane looked up and flashed a low shot beyond Fraser Forster.
Southampton striker Manolo Gabbiadini was inches away from an equaliser with a shot that shook the side-netting but the Italian limped off shortly afterwards with a groin injury.
As he trudged off in the 30th minute Dele Alli was fouled in the area by Southampton skipper Steven Davis and Alli picked himself up to stroke home a penalty to put Spurs two up.
It was no cruise though for the hosts as Southampton halved the deficit six minutes after the break when former Saints defender Toby Alderweireld failed to cut out Nathan Redmond's cross and James Ward-Prowse prodded a shot past Hugo Lloris.
Tottenham were edgy after that as Southampton sensed a route back in but despite their prodigious work-rate could not carve out too many goalscoring chances.
Substitute Vincent Janssen nearly calmed Tottenham's jitters with ferocious blast that Forster beat away while at the other end Sofiane Boufal rifled a shot just wide in the last minute.
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