Watch the best of Liverpool 5-0 win
The home side took control with two first-half goals, both neat close-range finishes from Rodriguez and Dirk Kuyt.
The Argentine winger volleyed in his second goal from a few yards out to kill the game just after the hour.
He then sealed his hat-trick with a low drive and substitute Joe Cole added the flourish with a shot that snuck in.
The result is a testimony to the optimism abound at Anfield these days, which is in stark contrast to the on and off-field gloom that characterised the respective reigns of former manager Roy Hodgson and ex-owners George Gillett and Tom Hicks.
There is a vibrancy about the Reds' play these days under Kenny Dalglish - evident from the off here through crisp passing and purposeful movement - and real intent in the boardroom, if reports of a £25m kit deal with American sportswear company Warrior prove accurate.
Qualification for the Europa League remains a possibility, with the club trailing fifth-placed Tottenham by three points, having played a game more.
As a testimony to the project Dalglish is undertaking on Merseyside, the Scot has willingly thrust a number of promising youth team players into the first team of late.
In the continued absence of talismanic midfielder Steven Gerrard, Jay Spearing again started here, while Jack Robinson stepped in for the injured Fabio Aurelio as part of an all-teenage full-back pairing with John Flanagan.
All three provided performances that belied their relative inexperience, with Spearing in particular an authoritative presence in the middle of the park.
It was he who played a vital role in the first goal, a seventh-minute body blow to Birmingham, who afterwards never looked likely to achieving the one win manager Alex McLeish feels they need to secure thair Premier League safety.
Spearing unleashed a venomous shot from 25 yards which goalkeeper Ben Foster allowed to slip from his grasp to the onrushing Rodriguez, who made no mistake with a close-range side-foot finish.
It would have been interesting to see how this Liverpool side would have responded had the sliding Cameron Jerome converted Stephen Carr's near-post cross to bring Birmingham level, but the striker failed to connect and not long after the home side doubled their lead.
Kuyt began and finished the move at the third time of asking, firstly flicking on to Suarez and then finally slotting home after goalkeeper Ben Foster had saved from Luis Suarez and also the Dutchman's first effort.
During his valiant attempts to prevent Kuyt's goal - the Dutchman's seventh in his last six league matches - the impressive Foster injured himself and after briefly attempting to carry on had to be replaced with substitute keeper Colin Doyle, making his first league appearance of the season.
The Irishman performed his first task well, saving a Suarez shot low down after the Uruguyan had ignored a well-placed Kuyt to shoot from 15 yards just before half time.
However, he was powerless to do anything about Liverpool's third - which despite their leisurely approach to the second half always seemed more likely than a Birmingham goal.
Last defender Carr's attempts to play Suarez offside from Martin Skrtel's long ball forward failed and, after advancing down the right, the Uruguyan had time to pick out Maxi Rodriguez at the far post for a straight-forward volleyed finish.
Shortly after, Rodriguez completed his treble with a low drive that rifled into Doyle's near post after his initial shot had been saved and Birmingham had failed to clear.
With five minutes remaining, Cole replaced Raul Meireles and with his first contribution cut in from the right and fired a low shot on goal that crept in past the flailing Doyle at the near post to add an emphatic slant to Liverpool's first league win over Birmingham since May 2004.
Source: BBC
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