Djibril Cissé set Liverpool on their way with a ruthless finish after 22 minutes. The peroxide poacher later gave way to Milan Baros, with whom he has so far struggled to form a partnership, and the substitute completed the victory with a splendid solo goal with seven minutes remaining.
With the other Group A fixture producing a goalless draw between Deportivo La Coruña and Olympiakos, Liverpool have established an early lead in what Benitez had predicted would be a very tight section.
The Liverpool manager was careful not to single out individuals, but he can only have been delighted by the performances of his three fellow Spaniards last night. Luis Garcia has become a Kop favourite with his deft linking play; Xabi Alonso was a dynamic foil for the playmaking of Steven Gerrard; and Josemi capped a solid display by providing an assist for the second goal.
Benitez, who had guided Valencia to victory by the same score in Anfield's previous match in the premier club competition, two years earlier, cut a buoyant figure afterwards. "You are normally satisfied when you win, but even more so when your team play well," he said. "I think we did that, and three points is a fantastic start."
Didier Deschamps, the Monaco coach and another Valencia alumna, did not attempt to disguise his disappointment. "A lot was expected of my players but they didn't deliver," he said. "But for our goalkeeper the defeat could have been a lot worse."
Injuries, suspensions and defections meant Monaco fielded only five of the 11 who started in last season's final defeat by Porto. They scarcely troubled Jerzy Dudek, the Pole's only concerns being a speculative early shot from 45 yards by Mohamed Kallon which flew over and a header by Emmanuel Adebayor which he caught easily with 15 minutes left.
Driven on by Gerrard, and with Garcia drawing gasps from the crowd with some exquisite touches, Liverpool overcame a tentative start and went ahead after a free-kick routine between Gerrard and Garcia. The captain's slide-rule pass and Cissé's delayed run were perfection itself. The former Auxerre striker, Houllier's £14m gift to his successor, combined power and placement.
Monaco, who had looked vainly in the linesman's direction, were soon doing so again as Garcia, sent clear by a flick of Harry Kewell's head, unleashed a shot which Flavio Roma blocked with his legs. The keeper had to save a header from the same player just before half-time, Garcia having again been supplied by Gerrard.
Garcia is not a classic No 10, operating more as a frontrunner, but his skill and stature make him well suited to the shirt. In contrast, Kewell was his usual frustrating mixture of sublime and ridiculous. Just before the hour, however, he released Cissé to run at Roma. The Frenchman took his time, as if weighing up the options, then bludgeoned the ball at the grateful keeper.
Monaco were always competitive, as one would expect of a Deschamps team, yet they were bereft of ideas other than the high ball in the direction of the towering Adebayor or the odd right-wing surge by Douglas Maicon.
Even so, Liverpool needed a second goal to extinguish any lingering Monaco hopes. Baros provided it in exhilarating style, chesting down Josemi's long pass and twisting round both Sebastien Squillaci and Roma before finding the net with a neat sidefoot finish.