The former England goalkeeper clawed away the Scotland international’s 64th-minute header on a night when Redknapp saw plenty to persuade him that his cause may not be a forlorn one.
Green replaced the injured Julio Cesar at the break and stood firm as the visitors turned in a spirited display against a side also desperate to steer clear of relegation.
And the new manager admitted after that he was satisfied with the result. “We worked hard,” he said “I felt we deserved a point. I was really pleased with the performance.
“We defended well when we had to. We denied them any chances and we had some good opportunities ourselves in the first half and we could have scored late on when Shaun Wright-Phillips did well.
“There were a lot of positives, so I’m pleased.”
He added: “On Monday, I picked the team and worked on the shape of the team. I thought the midfield looked strong tonight, the three lads looked powerful and bags of ability.
“There were some good points that came out of the match so I feel more optimistic than I did on Saturday. Tonight was good for us.”
QPR face fellow relegation candidates Aston Villa at Loftus Road on Saturday, and Redknapp believes getting the supporters behind the team will help create an intimidating atmosphere for the visitors.
“It’s all about confidence. That’s the key. I’ve got to keep encouraging them. There’s no point knocking any of them because when you’re bottom of the league, confidence is low,” he added.
Ultimately, Redknapp’s men failed to get a first league win but a fifth point of the campaign extended the Black Cats’ run to just two wins in 21 outings.
Redknapp’s men, of course, had an opportunity to try to persuade their new manager that they have a part to play in his brave new world at Loftus Road, and Adel Taarabt in particular seemed keen to take up the challenge.
He produced much of what was admirable about the visitors’ attacking play to link well with frontman Cisse, and it was perhaps significant that for much of the half, it was Black Cats left-back Danny Rose who was Martin O’Neill’s most enterprising performer.
Cisse might have got Rangers off to the perfect start when Taarabt picked him out unmarked at the far post with a fourth-minute cross, but his downward header lacked power and direction and ended up in the arms of Mignolet.
Mignolet was extended much further with 12 minutes gone when, after Taarabt has twice combined with Esteban Granero, Cisse curled a right-foot shot towards the bottom corner and saw it tipped around the post at the last minute.
The home fans were growing restless and their mood did not improve when Mbia was given time and space to drill a 25-yard effort just past the post.
However, it was opposite number Green who had to demonstrate his enduring quality with 64 minutes gone when Fletcher met Sebastian Larsson’s inswinging corner with a downward header which seemed destined for the net until the keeper somehow managed to block one-handed and then clutch it to his body.
Rangers might have snatched victory late on through substitute Shaun Wright-Philips but Mignolet was equal to the challenge.
SUNDERLAND: Mignolet, Bardsley, Kilgallon, Cuellar, Rose, Larsson, Cattermole (Colback 6), Gardner (Saha 78), Johnson (McClean 70), Sessegnon, Fletcher.
QPR: Julio Cesar (Green 46), Bosingwa, Hill, Nelsen, Traore, Granero, Mbia, Diakite (Park 65),Taarabt (Wright-Phillips 77), Mackie, Cisse.
Ref: Andre Marriner (W Midlands).