The Hatters, the only representative in the Carling Cup from League One, had more than matched their Premiership opponents for much of a high-tempo encounter.
But Cahill's killer-instinct proved decisive as he struck in the 11th minute of extra-time to send the Toffees through to the quarter-finals.
Luton, beaten only once at home all season, kept faith with the same 11 that saw off Nottingham Forest 2-1 on Saturday while Everton made six changes to the side that beat Derby 2-0 on Sunday.
Having already dumped Sunderland and Charlton out of the competition, the Hatters started the game in confident mood with David Bell twice firing just wide from long range in the opening ten minutes.
The home side were stalled just 20 minutes in however when leading goalscorer, 39-year-old Paul Furlong, limped out of the action to be replaced by Calvin Andrew.
That reduced Luton's threat in the final third and, despite bossing possession, Town could not trouble Everton's second-choice shot-stopper Stefan Wessels with a shot on target in the opening 45 minutes.
Instead it was the visitors who almost opened the scoring on the stroke of half-time when a rare slip from Jaroslaw Fojut allowed Victor Anichebe to run on to Phil Jagielka's pass and cross for the onrushing James McFadden, who was only denied by Chris Perry's lunging challenge.
Unperturbed, Luton started the second period as they did the first and Bell was again unlucky with a 12-yard shot on the turn that flew wide in the 49th minute.
However, from that point on the tide began to turn and, after Fojut was booked for a foul on Steven Pienaar in the 51st minute, Dean Brill had to be alert to tip Leon Osman's 25-yard shot over the bar from the resulting quickly-taken free-kick.
Nuno Valente fired a 25-yard shot just over in the 55th minute and visiting skipper Alan Stubbs hit a 22-yard free-kick inches past the post three minutes later.
Luton then had two lucky escapes in a matter of seconds just after the hour mark as Osman's angled shot deflected off Alan Goodall only for Brill to save with his foot.
And then Joleon Lescott turned Perry in the penalty area, but dragged his right-foot shot past the far post.
Jagielka, who had endured a nervy first half, saw a header hacked off the line following a McFadden corner in the 63rd minute and the former Sheffield United man then had a header held by Brill after another McFadden flag-kick five minutes later.
Luton did manage to rally and Andrew should have done better than completely miss Darren Currie's corner in the 75th minute when only a touch with his head would surely have seen the striker find the net.
Everton substitute James Vaughan was guilty of an equally as glaring miss two minutes later when he ran in unmarked on to Jagielka's right-wing cross only to place his header wide from 14 yards.
With both sides going for a winner in normal time, Osman forced Brill to save with his legs in the 84th minute before Bell's ferocious cross from the right two minutes later almost deflected in off Stubbs.
As the game went into extra-time, Cahill was at his predatory best to net the winner in the 101st minute as fellow substitute Thomas Gravesen's corner found its way to the far post where the Australian was on hand to convert.
The Hatters still didn't give up and Spring's shot had to be cleared off the line by Lescott with seven minutes remaining before Andrew failed to convert substitute Dean Morgan's cross four minutes later.