Redknapp masterminded Tuesday's goalless draw at Sunderland, going some way to stopping the rot that had cost Mark Hughes his job as manager.
The clean sheet was only Rangers' second of a league campaign that has seen them make the worst start of any team in the division's history.
Aston Villa's win over Reading yesterday also meant Redknapp's new side ended the evening eight points adrift of safety after 14 matches.
But veteran defender Nelsen was confident afterwards that if anyone could rescue the club from the drop, it was the man who performed similar feats at Tottenham and Portsmouth.
Both clubs went on to thrive in the Premier League, with Nelsen playing under Redknapp at Spurs last season en route to them finishing in fourth place.
The 35-year-old said: "I know Harry and that him and his staff will be doing their utmost to get us points.
"Obviously, he hasn't had much time. He is still getting to know every player.
"He has to cast his own eye on everyone and that won't happen overnight. He is just trying to keep everyone positive.
"None of us has been in this position before.
"It's horrible, but Harry will bring in his own ideas, bring in some confidence.
"We just have to start producing on the field and get some points."
QPR are winless with more than a third of the season gone and Nelsen admitted they needed to win at least 10 of their remaining 24 games to stand any chance of survival.
They went close to getting the first of those victories last night, having arguably been the better team against fellow strugglers Sunderland.
"Of course, it is going to be very difficult but anyone watching us against Sunderland would not have known which side were at the bottom of the table," Nelsen said.
"We will have to get 10 more wins at least.
"We can't worry about other teams winning or losing.
"We just have to concentrate on ourselves and just try to win as many games as we can.
"That's all we have to do, try to go on a run, try to secure wins and points and after 38 games we will just have to see where we are."
QPR finally sent out an SOS to Redknapp last week after agonising over sacking Hughes.
The Welshman was said to have made a real impact behind the scenes at Loftus Road as Rangers bid to become a Premier League club both on and off the field.
New Zealand captain Nelsen has particular reason to be grateful to Hughes, who brought him to English football from Major League Soccer almost eight years ago.
The pair spent three-and-a-half years together at Blackburn and were reunited this summer when Nelsen moved to Loftus Road after being released by Spurs.
"It was very sad to see Mark go because he has transformed QPR," Nelsen said.
"It may not look like it from the outside but, inside, it's a different club.
"It's a Premier League club now but, unfortunately, the results didn't go for him and I felt really bad for him.
"Harry has come in and his credentials speak for themselves.
"It is up to us now to bring in results for him, start producing on the field and getting some points."