But they were put under severe pressure in the second half before Jose Reina could claim another clean sheet, the 54th in his first 100 games for the club a new Liverpool record.
Torres, scoring on his sixth successive home match, equalling a club record, won praise from boss Benitez, who said: "We must admit that we are surprised by how well Fernando has settled here.
Benitez said: "We needed to show discipline, that was very important, as well as being well organised.
"We were put under some pressure after the break, but we showed character throughout.
"However, I do not believe that we are sure of fourth spot just yet. We are at Arsenal next Saturday and that will be tough, while Everton are at home to Derby. Things can change around very quickly."
Moyes expressed his own disappointment at the way Everton conceded the winner to Torres, and Ayegbeni Yakubu's error that cost his side dearly.
Moyes said: "I was disappointed by the way we gave them their goal, and I think Yakubu was upset and maybe affected himself by what happened.
"He was caught in possession and should have cleared the ball. But we should not have rushed out like we did until we knew the ball had been cleared properly. We were in advance of the ball at that stage, and that was naive.
"That goal gave them the impetus to go forward, and we had to hang in there until the break. But we did that without conceding another goal.
"And we gave it everything after the break. But we were without so many attacking players injured, and also missing Tim Cahill for the same reason, and he is someone who could have been used in support of Yakubu.
"Basically we did not have enough going forward to really worry them. But we must still believe we can catch them, I am sure that the teams below us still feel they can catch us, so we must believe we can do the same with teams ahead of us."
Moyes added: "Any team with a five-point advantage at this stage must consider it a great advantage, but we will fight on."