Tottenham badly missed the presence of key defender Dean Richards in the centre of defence after he failed to overcome a niggling Achilles problem and were always struggling after going behind in only the 12th minute.
Goalkeeper Kasey Keller failed to hold Beattie's fiercely struck free-kick and Michael Svensson was on hand to bundle home the follow-up from close range.
Keller had to move swiftly in the 33rd minute to keep out substitute Anders Svensson's low 25-yard drive although Tottenham were unlucky not to go into the half-time interval level.
Robbie Keane's shot from the edge of the area was deflected off Claus Lundekvam but went inches wide with keeper Antti Niemi stranded.
Tessem lashed home the second after being put through by Beattie before Anders Svensson was allowed to run 40 yards before burying the third under Keller.
Keane had forced a fine save from Niemi and also missed an open goal as Southampton relaxed and Tottenham looked for some way back into the tie.
But Beattie deservedly added his name to the list of scorers with ten minutes left on the clock when he fired home his 14th goal of the season after Keller had saved his initial header.