The Toffees took the lead inside the first five minutes from a Ross Barkley free kick which evaded everyone and found the far corner past Hugo Lloris' despairing dive. Lloris didn't last until the half, though, as Michel Vorm came on to replace the goalkeeper, who suffered a hamstring injury while chasing down the ball.
Spurs were back level shortly after the break as Erik Lamela headed home a Kyle Walker cross and applied the late pressure as Stekelenburg palmed away a close-range shot from Janssen, saw Eriksen's free-kick go onto the roof of his net and brilliantly tipped away a Lamela effort that deflected off Mason Holgate.
Southampton were held to a 1-1 draw Watford as Nathan Redmond netted on his debut for the club.