Rodriguez's impressive early opener was followed by Dirk Kuyt's seventh goal in his past six Premier League games to set Liverpool on their way.
The Argentina midfielder completed his treble with two fine finishes after the break and there was a late fifth from Joe Cole.
Liverpool remain sixth, four points behind fourth placed Manchester City, and this encounter added further weight to the idea that Dalglish can return the Reds to the summit of the English game.
But it was Rodriguez's showing that caught the eye of former Liverpool striker Dalglish, who knows a thing or two about what it takes to succeed at Anfield.
"I think we were deserved winners and I think we played some fantastic football during the game as well," Dalglish said. "So for us, we've had a good day and it's very enjoyable.
"Maxi's a very intelligent footballer and as we've said before, the way the boys have worked in training has been a real credit to themselves in the way they've adapted to it.
"He's not played for a few weeks but he came in and did a fantastic job for us.
"Players are going to play better if they're confident. Also if they're happy going to their work, they're going to produce better results.
"I think it's a combination of those two factors and probably a lot of other ones as well.
"The fact that they're playing with players that know how to pass it to the same colour of jersey as each other helps."
Dalglish only has the Liverpool job until the end of the season but it seems a matter of time until he is re-appointed as the Reds manager on a full-time basis, not that he is willing to discuss the matter at the moment.
"There's nothing to add. When we've got something to say, we'll say it. At this particular moment in time, it's the fifth amendment," he added.
Rodriguez gave Liverpool an early lead as Ben Foster failed to hold on to a Jay Spearing blast and he was on hand to pounce from close range and clip past the Birmingham goalkeeper.
And as the half progressed, Liverpool did get on top and began controlling the game as their dominant midfield over-ran the visitors.
A second goal always felt inevitable and so it proved when Luis Suarez showed impressive power and pace to charge through on goal and although Foster made two fine quickfire saves, the ball eventually fell to Kuyt, who swept in from 12 yards out.
Following the interval, a long ball was picked up by the brilliant Luis Suarez, who was played onside by Stephen Carr, and his superb cross found Rodriguez, who volleyed home.
Rodriguez's amazing afternoon was not finished there either as he then grabbed the match ball as Birmingham fell to pieces at the back.
His long-range shot was well stopped by Colin Doyle but the rebound fell nicely for Rodriguez before Cole added a fifth just before the end as his low shot just squirmed in to make Birmingham?s afternoon even worse.
"You come here to try and frustrate Liverpool and the home fans and set out so to lose the goal so early disrupted us totally," Birmingham manager Alex McLeish said.
"To be fair, the first two goals were really soft and we have to do better and I don't think anybody would disagree with that."
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