The England international goalkeeper replaced Julio Cesar when the Brazilian suffered a dead leg in the second half with the game balanced at 1-1.
Jay Bothroyd put Rangers ahead, then Green preserved the lead with a point-blank save to stop Maya Yoshida's goal-bound header.
"Let's give him credit," said Redknapp, "Rob came off the bench stone-cold and made a world class save, so a lot of credit goes to him."
Redknapp returned to the club he managed for 12 months for the first time since his resignation in December 2005, but he shrugged off a hostile reception to praise a resilient performance from his side that earned just their third win of the season.
"All I wanted today was to come here and try to get a win, whether it was here or anywhere else we needed a win. It was a great result for us.
"I picked a team that worked today, a team where everybody was going to work. We didn't have anybody not working. When we didn't have the ball, everybody worked.
"That is the only way anybody can win football matches, everybody has to put a shift in. I decided to pick a team today that would do that for me. I thought they responded, and the subs that came on did the same. All round it was a good performance."