Mohamed Salah put the Reds in front after just three minutes on Merseyside, latching onto a loose backpass from Eric Dier and steering beyond Hugo Lloris.
The hosts held onto that advantage until the 80th minute when substitute Victor Wanyama found the top corner from range with a thumping half-volley after Loris Karius had punched clear a cross into the six-yard box.
However, the drama was only just beginning to unfold in L4 as Spurs were handed a penalty shortly after – but Karius held his nerve to repel Harry Kane’s blast down the centre.