The Reds' stand-in strikers shrugged off the absence of Fernando Torres to secure a comfortable victory make it an unhappy return to Anfield for former Reds manager Gerard Houllier.
With Torres given the night off to be with his wife Olalla, who had gone into labour with their second child, Ngog and Babel ensured he was not unduly missed with first-half goals.
Rodriguez added the third in the 55th minute to make it four successive Premier League victories for Liverpool at Anfield.
In truth Villa, like previous visitors West Ham, posed little in the way of a threat but there were some encouraging performances from Liverpool all the same.
Raul Meireles, having been given an extended run in the centre in the absence of the injured Steven Gerrard, is starting to look like an £11million midfielder and was in the midst of most of the hosts good play.
Ngog and Babel will also have gained plenty of confidence from their performances, although they will have to prove they can do it against better opposition than this if they are to have long-term futures at Anfield.
Almost forgotten in all the attacking play was Jose Reina's clean sheet, his 100th in 198 league matches breaking by some considerable distance the previous record held by Reds great Ray Clemence - who took 217 games to reach the landmark.
Houllier, who won five trophies in his six-year spell at Anfield - and four alone in 2001 - to cement his place in the club's history books was welcomed back by a club motif-emblazoned banner on the Kop which read Gerard's Heart Beats.
It may have skipped a beat in only the third minute when Dirk Kuyt volleyed wide after Ngog's two headers from Meireles' right-wing free-kick were not cleared.
Set-pieces were a weakness for Villa all night and they were undone by one in the 14th minute.
Meireles' clipped delivery picked out Martin Skrtel who speared a header back across goal and the diving Ngog could not fail to nod in from barely three yards.
It was the Frenchman's eighth goal of the campaign - although only his second in the league - and it took him past Gerrard as the club's leading scorer this season.
Two minutes later Liverpool had doubled their lead with Babel justifying manager Roy Hodgson's faith to select him up front.
The Dutchman has consistently failed to impress since his £11.5million move from Ajax in 2007 but his goal was an example of the talent - which some would argue he has wasted - at his disposal.
Playing on the shoulder of Stephen Warnock, Babel allowed Lucas Leiva's lofted ball to drop out to his right and he swivelled to smash a shot across Brad Friedel and inside the far post.
Sotirios Kyrgiakos could have made it 3-0 in the 27th minute but planted wide his far-post header from Meireles' free-kick while Babel curled a first-time shot just wide of Friedel's left-hand post from the Portugal international's low cross.
Villa had one chance to get back in the game just after half-time but Gabriel Agbonlahor's close-range shot from Stewart Downing's cross was half-saved by Reina and the ball cleared by Paul Konchesky.
Moments later a counter-attack of brilliant simplicity finished them off.
Reina collected and instantly rolled the ball 30 yards down the middle of the pitch to Rodriguez, who offloaded to Ngog out to the left and then perfectly timed his run to sidefoot home the return pass 40 yards further up the pitch.
Rodriguez looks increasingly at home out on the left and, having scored just one goal in his first five months after joining last January, he now has three in his last seven matches.
Only former Liverpool goalkeeper Friedel prevented a fourth, parrying away Johnson's shot after he had weaved his way into the area.
Kyrgiakos' header from Meireles' corner was cleared off the line by Jonathan Hogg as Villa threatened to buckle completely.
The Kop, as in years gone by, sang the names of Houllier and his assistant Gary McAllister but it was more out of sympathy than anything else.
Hodgson, who has yet to win over the Anfield faithful, stood unmoved on the touchline safe in the knowledge three points were safe - which Houllier would testify is how all managers are ultimately judged.