Adam Lallana had an opportunity for Southampton two minutes later, but his effort was high and wide of the crossbar.
The Saints had the ball in the back of the net after nine minutes when James Rodriguez converted from close range, but the offside flag had been raised.
Rodriguez did not have to wait long for a goal to arrive, however, with the England international slotting into the bottom corner after 19 minutes.
Southampton had their second just before the half-hour mark when Lallana found some space inside the box and slotted his effort into the bottom corner.
Nabil Bentaleb had a long-distance effort for Spurs moments later, but it whistled wide of Boruc's post. The hosts were level after 31 minutes, however, when Christian Eriksen struck home from close range.
Both sides had chances in the latter stages of the half - including opportunities for Lallana and Eriksen at either end - but 2-1 to Southampton remained the score at the break.