Richarlison's header and Gylfi Sigurdsson's rebound finish after Kepa Arrizabalaga saved his penalty gave Marco Silva's side a vital win in pursuit of a top half finish .
Chelsea dominated the first half; Eden Hazard hitting the post and Ross Barkley, Pedro and Gonzalo Higuain all being denied from close range.
Everton took full advantage of their reprieve as the visitors failed to build on their dominance in the opening 45 minutes, producing a lacklustre display after the break.
Rudiger compared the performance to the draw with Wolves a week ago , in which Chelsea needed a late Hazard goal to rescue a point, and slammed the performance of his team-mates.
"It is like the same game as against Wolverhampton, only we lost," the German told Sky Sports .
"We played a good first half, the only thing you could say is if you could have scored one or two.
"We didn't and it is unacceptable the way we came out and we lost the game in 10 minutes.
"We were passive and if you are passive against any opponent in this league it is dangerous.
"At the end of the day we played well in the first half but we didn't score but the way we approached the second half is unacceptable.
"There is frustration. Everyone deals with it differently but it is just unacceptable.
It could now be that the club's best route back into Europe's premier club competition is via the Europa League - where they face Slavia Prague in the quarter-finals .
The ex-Roma centre-back added: "We still we have eight games to go but we cannot say next week, next week, next week have to do better definitely because this match you are not allowed to lose it."