The little Argentinian was not necessarily brilliant but just put himself in the right places to capitalise on some impressive team play by a side brimming with the confidence instilled by Reds boss Kenny Dalglish.
There were positives all over the field with Dirk Kuyt scoring his seventh goal in six league matches while even substitute Joe Cole, who has endured a disappointing maiden season, got among the goals with a late deflected effort.
Five goals and all this achieved without £35million record signing Andy Carroll, who was unavailable due to an injury sustained in last Sunday’s draw at Arsenal which allowed Kuyt to move back up front.
Adaptability was the name of the game as the Reds adopted a midfield diamond formation to get the best out of Raul Meireles’ attacking intent.
Crucial to making it work, however, were the superb Lucas Leiva at its base and Rodriguez and Jay Spearing.
Rodriguez is becoming something of a lucky charm for the side he joined in January 2010 as although his goals are few and far between – just seven in 49 matches – they have all coincided with victories.
He is more suited to the midfield set-up which Kenny Dalglish went with at the start but it also brought the best out of Spearing, who had a hand in the opening goal – although not as much as Foster in the seventh minute.
Kuyt’s lay-off saw the 22-year-old midfielder fire in a swerving shot which the Birmingham goalkeeper spilled into the path of Rodriguez who made no mistake from close range for his first goal since December 3.
Birmingham briefly responded, without really threatening, before they were caught by a classic Liverpool counter-attack in the 23rd minute.
Jose Reina intentionally picked out Meireles just over the halfway line and he flicked on into the path of Luis Suarez who did well to hold off the challenge of Martin Jiranek.
Foster may have been at fault for the first but he saved well from the Uruguay international and again from Kuyt’s follow-up but he could do nothing to prevent the Holland international getting up to slot home the rebound.
The England goalkeeper injured himself in the process and was replaced 10 minutes later by Colin Doyle, who watched one Kuyt header sail across goal and wide of the far post before gratefully clasping Suarez’s shot to his chest just before the end of the half.
Almost unnoticed in all the pass-and-move mayhem Liverpool were creating was the performance of the Reds’ teenage full-backs, 18-year-old John Flanagan on the right and Jack Robinson, a year younger.
The latter certainly did not look like a youngster making his first start after two substitute appearances 11 months apart when, in the opening minutes, he coolly dispossessed the far more experienced Alexander Hleb as Birmingham threatened an early attack having swept through the inside-left channel.
Having moved into a comfortable 2-0 lead Dalglish almost immediately reverted to more orthodox 4-4-2 formation to ensure Blues were afforded no way back.
Alex McLeish’s side provided more of a challenge in the second half but were always chasing the game and their cause became a lost one in the 66th minute when Rodriguez scored his second.
Suarez was played onside by Carr, trailing slightly behind his defensive colleagues, and the forward raced onto Martin Skrtel’s pass and crossed to the far post where Rodriguez side-footed home.
Rodriguez saved his best goal for last, collecting Suarez’s 73rd-minute pass and shooting low at Doyle who half-saved his effort only for Meireles to force the ball back into the danger area for Rodriguez to convert.
There have not been many instances since his arrival when Suarez has been outshone and as if to remind people of his talents the Uruguay international produced an audacious behind-the-leg shot which would have really rubbed salt in Birmingham’s wounds.
That honour was left to Cole who, within seconds of replacing Meireles, cut in from the right to hit a deflected shot past Doyle for the fifth.
While this result was a barometer of the confidence at Anfield it will have done little for spirits within the Birmingham camp, with the club still looking over their shoulders five points above the relegation zone.