Substitute Dan Gosling curled the winner with just three minutes remaining in what turned out to be a miserable night for Liverpool in the FA Cup.
Steven Gerrard went off with an injured hamstring after just 15 minutes in a poor first half littered with fouls.
Chances were few until the second half when Everton came more into the game after the dismissal of Lucas in the 76th minute for a second yellow card.
Leon Osman had already hit a post for the Blues but with the man advantage they poured forward hoping to avoid a penalty shoot-out.
But in the 117th minute Gosling collected a right wing cross from Andy van der Meyde and momentarily seemed to have missed his chance. But the 19 year old found space and with the aid of a slight deflection curled the ball home for a deserved winner.
"It was a great feeling. Not just for me but all a Everton football club," the goalscorer told ITV1.
"I just thought shoot, get it on target, and thankfully it went in.
"I was bit nervous but had a few nice touches and I've had a taste of the big games in the past and all the lads are very encouraging."