Benitez was sworn in to replace the beleaguered Steve McClaren on Friday, but lost his first game in charge four days later against Premier League leaders Leicester City.
Despite the result, Newcastle remain just a point behind their North East rivals, who are 17th in the table, ahead of Sunday's derby.
With an eight point gap between Sunderland and Swansea City above them, it is reasonable to assume that only one of the two rivals will survive relegation to the Championship.
Redknapp agrees, barring a 'big run' or form for both clubs, and feels that with Benitez on board Newcastle may just have the edge over the Black Cats and Norwich City.
"It looks like two from three are going to go along with (marooned bottom-club, Aston)Villa," the 69-year-old told talkSPORT's Alan Brazil Sports Breakfast Show on Thursday. "One of the big ones, Sunderland or Newcastle look like they’re sure to go unless they go on a big run.
"Everybody, every year will go: Sam’ll keep you up, Sam’ll keep you up but it’s going to be difficult obviously with Benitez coming in.
"I’ve got to be honest I think Newcastle will stay up again somehow, just about creep up.
Ominously for Newcastle, ahead of this weekend's clash at St. James' Park, they've lost the last six in a row against their Tyne-Wear rivals, scoring just once in that time.