Pompey looked destined to drop out of the Premier League at this stage of the 2005-06 campaign, but under Redknapp's guidance they strung together a tremendous sequence of results to take 20 points from their last 10 games and retain their top-flight status.
QPR's 4-1 defeat at Swansea on Saturday means they remain rooted to the foot of the top-flight table, six points from safety with 12 games left.
The second hammering of the season against the Swans ended an unbeaten run of five league games, and Redknapp knows the Rs need to quickly add to their meagre tally of two league wins.
He said: "I am confident we can survive. I know it is going to be hard, and I think it will go to the wire but it is not impossible.
"It is very similar to the situation I had with Portsmouth, it is much the same if you look at the stats.
"I think that was down to the last 10 games that we got out at Pompey with 20-odd points. That is what we need here, it's not impossible."
The Rs have not scored twice in a Premier League game since mid-December, and have scored just 19 in total from 26 games, the lowest tally in the top-flight.
Redknapp admits he is short of striking options, with the hip problem hindering Bobby Zamora - who got their only goal at the Liberty Stadium - a particular concern, while France striker Loic Remy has missed the last two games with a groin strain.
"We have a chance if Remy can come in and score some goals and show what he can do, and we can get Bobby out on the pitch," he said.
"The problem with Bobby is we have to stop him at half-time. If we played straight through he could probably manage 70 minutes, but stopping at half-time he seizes up then he can't move.
"When he plays he's different, he can move, hold the ball up, he is someone we can play up to. Without him we don't have someone who can lead the line."
But while the former West Ham, Southampton and Tottenham boss remains bullish about QPR's chances of avoiding the drop, he readily admits it is not a situation he is relishing.
"It is difficult. It is horrible," he said.
"I watch every result, every game, kick every ball. You can't worry about other teams - they want us to lose and we want them to lose. That's life.
"I can't say 'Wigan have won, jolly good' because I like Roberto (Martinez). I just thank God he got stuffed against Chelsea."