Green has come to the fore in the absence of Michael Dobson
Hull KR put an end to their recent poor form and condemned Leeds to a fourth defeat of Super League XVI with a 38-28 win at Craven Park.
Lee Smith opened the scoring for Leeds before Kallum Watkins and Kevin Sinfield's boot made it 10-0 to Rhinos.
But Michael Vella sparked the fightback with Kris Welham, Matt Cook and Scott Murrell adding tries before half time.
Leeds added Ryan Hall and Paul McShane tries but Rovers answered through Liam Colbon, Sam Latus and Blake Green.
Both sides were understrength with Leeds missing seven regulars from their line-up.
But it was not obvious from the start when centre Lee Smith, back from a hamstring injury, took a return pass from his winger, Watkins, to score and then Watkins gathered Sinfield's kick to the corner for his seventh try of the campaign.
Sinfield could only convert one score and on 18 minutes it Rovers' captain Vella who sparked his troops into life.
He gathered Galea's pass and wrestled his way over for his first try since the summer of 2009 and then stand-in kicker Murrell landed the first of his five goals.
Green came to the fore in the match as he had a hand in the next two scores.
First he broke clear to put Welham away and then timed a defence-splitting pass to perfection to put substitute Cook in for his try.
Five minutes before the break Ben Cockayne fashioned Murrell's try when he took Ben Fisher's offload although his pass had a hint of being forward.
Murrell converted his own try to make it 24-10 at the turn around.
Two minutes into the second half Latus made a 70-metre break to set up winger Colbon in the corner but Leeds looked like they might fight back when Hall crossed for their third score and Sinfield added another goal.
But Green displayed his influence once again when he had a hand in Latus's try and then Galea's score.
Brent Webb produced a reverse pass to put McShane over and Watkins won a late kick-chase for his second but by then Rovers' victiory was beyond any doubt.
Hull KR coach Justin Morgan: "I have been saying we were not far away and today was evidence of that.
"For 80 minutes we were pretty good. The players showed determination on the back of two fairly intense weeks of training.
"We had to lift the intensity and we saw the results of that. I'm very proud of the players and I put the credit at their doorstep.
"They're the ones who turn up and train every week. I'm happy for them that they got a result over a very good team.
"We scored some lovely tries and our defensive technique improved. The order will be more of the same next week. We have to back it up against Wigan."
Leeds Rhinos coach Brian McDermott said: "We got a couple of highly-skilled tries but I wouldn't say we started so well.
"The word 'soft' is the one I've got in my head. You show that to any opposition and they go straight for your throat and Hull KR did that.
"There were a few individuals who stood up but as a group we were soft and I include the coaching staff involved in this."
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