Steven Gerrard created two of the goals and new boy Glen Johnson had an outstanding game surging down the right at will.
Benitez bought Johnson, he claimed, to provided that extra adventure in difficult home games. And the England defender underlined just what his new manager meant.
He scored a close-range goal on half-time on his home debut, to add to Fernando Torres’ fourth-minute opener, and aided Gerrard’s advance to set up the third for Dirk Kuyt.
Johnson’s run and cross in injury-time presented substitute David Ngog with the fourth to cap an outstanding home debut for the new full-back.
Spanish youngster Daniel Ayala made his full Liverpool debut, with Martin Skrtel failing to recover from a damaged jaw sustained in Saturday’s defeat at Spurs.
Liverpool fans’ group, the Spirit of Shankly, organised a mass distribution of red cards ahead of the game to be waved by supporters protesting at the George Gillett-Tom Hicks ownership of the club.
Resentment runs deep at Anfield at the financial mess the club are in and Benitez’s limited transfer budget.
But it was his record signing, Torres, who struck quickly to give the Reds the lead.
Lucas Leiva had seen a skidding 20-yarder held by Thomas Sorensen before Liverpool were ahead after just four minutes.
Gerrard burst through on the right to pull the ball back for his Spanish side-kick to drill past a helpless Sorensen.
Kuyt and Torres had shots saved and from a 44th minute corner they struck again. Kuyt’s low header was blocked by Sorensen on the line and the ball fell for Johnson to hook home from six yards.
Stoke came out after the break determined to get back into the game. A string of dangerous corners resulted in Jose Reina making an outstanding save to his right to keep out a fierce Delap drive. But Liverpool increased the tempo of their game and were running at Stoke from all angles.
The third goal arrived after 78 minutes, with Johnson sending Gerrard into the box with a clever pass. The Liverpool captain powered on to drill in a low cross which Kuyt slid past Sorensen from close range.
Liverpool sent on Andriy Voronin and Albert Riera for Gerrard and Kuyt with nine minutes left, then three minutes later Ngog replaced Torres.
And it was Ngog who headed home from under the bar after another fine run and cross from Johnson had deflected into his path in injury-time.
LIVERPOOL: Reina, Johnson, Carragher, Ayala, Insua, Mascherano, Lucas, Kuyt (Riera 82), Gerrard (Voronin 81), Benayoun, Torres (Ngog 84).
STOKE: Sorensen, Wilkinson, Shawcross, Abdoulaye Faye, Higginbotham, Delap, Whelan, Whitehead (Pugh 69), Etherington, Beattie (Fuller 62), Cresswell (Lawrence 62).
Referee: Peter Walton (Northamptonshire).