Cahill's extra-time strike sees Toffees battle past plucky
And Cahill struck in the 101st minute as Everton made the last eight of a cup competition for the first time under Moyes.
Luton will feel hard done by after dominating the first half and frustrating their visitors throughout the second.
They started with the evergreen Paul Furlong as a lone striker and the 39-year-old was soon busying himself, winning an early free-kick from a foul by Lee Carsley which David Bell blasted just inches wide from 25 yards.
Bell crashed another long-range shot past the post and Matthew Spring volleyed over, before the Toffees registered an effort on target with Leon Osman’s curler failing to trouble Dean Brill.
After the break Bell was again first to react as Everton failed to clear Currie’s free-kick, the winger hooking his shot across goal and wide.
But the Toffees showed a rare moment of invention in the 50th minute when a free-kick gave Osman a shooting chance and Brill did well to tip his effort over the crossbar.
Everton almost made the breakthrough in the 58th minute when Stubbs drilled a low free-kick through the Luton wall only to see it fly wide of Brill’s right-hand post.
In extra time, Moyes sent on Thomas Gravesen and 11 minutes in the goal finally arrived from the on-loan Celtic midfielder’s corner.
The cross deflected off a Luton head to the far post where Cahill was lurking to prod the ball past the helpless Brill.
Brill, Goodall, Perry, Coyne, Fojut, Bell, Currie (Morgan 104), Robinson, Spring, Furlong (Andrew 20), Edwards (McVeigh 104).
Wessels, Lescott, Stubbs, Jagielka, Nuno Valente, Neville, Pienaar (Gravesen 94), Osman, Carsley, McFadden (Vaughan 71), Anichebe (Cahill 77). Referee: Steve Tanner.




