Liverpool manager Rafael Benitez hailed his side's 1-0 victory in the 213th Merseyside derby as "massive".
Dirk Kuyt's close-range header 10 minutes after half-time proved the difference as the Reds played the last 55 minutes with 10 men after Sotirios Kyrgiakos was dismissed for a two-footed challenge on Marouane Fellaini.
Everton failed to capitalise on their numerical advantage and they had Steven Pienaar sent off for a second bookable offence in the fifth minute of second-half stoppage time.
Liverpool are now unbeaten in their last seven league matches, having kept six clean sheets and accrued 17 points to put them firmly back in the race for Champions League qualification.
"It was massive for us. To win in a derby is really important - to win in a derby with 10 players at Anfield is more important," said Benitez. "I was really pleased for the players and the fans because everyone was working so hard that I think at the end we deserved to win.
"From the beginning we were doing well in terms of work-rate and after [the sending-off] it was amazing to see all the players working so hard, defending and also going forward and trying to score."