Christian Eriksen opened the scoring with an excellent goal on 14 minutes, striking a low left-foot shot past Fraser Forster from 20 yards, who was then beaten from the penalty spot by Dele Alli on 32 minutes, the England midfielder picking himself up to convert from 18 yards after being fouled by Steven Davis.
Southampton pulled one back six minutes into the second period when James Ward-Prowse found himself free at the back post and tucked home past Hugo Lloris.
After an entertaining first half, the second was much more attritional as we had to dig in against a determined Southampton fightback, with neither side really creating clear-cut chances.