Newcastle, who have fellow strugglers Birmingham, Fulham and Reading in their next four games, were hanging on until a freak Jermaine Pennant goal two minutes from the break, with Fernando Torres doubling the lead a minute later and Steven Gerrard wrapping up the scoring in the 51st minute.
Benitez hailed Liverpool's fourth successive league victory as "just perfect" as his team took a firm grip on fourth place.
The Spaniard was delighted with the growing partnership of Gerrard and Torres, and was able to withdraw them both in the second half to rest them in preparation for Tuesday's Champions League trip to Inter Milan.
Benitez explained: "I must be happy with a performance like that.
"Three goals, three points, nothing conceded and I was able to rest key players ahead of the Champions League.
"In every way it was just a perfect day for us. Our confidence is growing, as is the partnership with Gerrard and Torres.
"They are working well and the other players are making sure they have the time and the space to show their quality and pace."
Benitez conceded that his team were put on the road to victory by the fortuitous 43rd-minute cannon off Pennant.
He said: "Newcastle had defended well and we were really lucky with our first goal.
"But we had been controlling the match and I felt we would have won anyway, whether that had gone in or not."