Tommy Miller and Julio Arca were on the scoresheet to guarantee the three points, Sunderland's first maximum haul since December 2002, which lifted the Black Cats into 19th place and sent Everton to the bottom.
Under-fire Everton boss David Moyes has received the dreaded vote of confidence from his employers despite the Goodison Park outfit slumping to the foot of the Premiership.
Everton lost 1-0 to Wigan on Saturday and Sunderland's 2-0 win at Middlesbrough on Sunday condemned Moyes's men to rock bottom position. Currently with Everton and Sunderland in the lower three is WBA.
Everton have lost six games in a row and eight in nine competitive matches.
They have also been knocked out of the Champions League and on Thursday they face Dinamo Bucharest in the UEFA Cup when they will attempt to peg back a 5-1 deficit from the first leg.