Jim Magilton's side were trailing to Aaron Mclean's early header but Routledge grabbed an equaliser before half-time to deny Posh their first win of the season.
Rangers fielded a team boasting three Premier League loanees, whereas Peterborough lined up with four players plucked from non-league, but it was the visitors who at times looked far more capable of challenging at the top end of the table this season.
Mega-rich Rangers are, once again, expected to push for promotion but Flavio Briatore's millions have yet to unearth someone to get on the end of all the flicks and tricks.
At least chairman Briatore was not present to witness an out-of-sorts showing from his expensively-assembled outfit, the Italian apparently having more pressing matters to deal with on the grand prix circuit.
Posh even thought they had grabbed a stoppage-time winner, but
Craig Mackail-Smith's effort was ruled out.
The west Londoners' did create the first chance, courtesy of their north London connection, as Tottenham loanee Adel Taarabt exchanged passes with Arsenal's Jay Simpson before shooting straight at Joe Lewis.
But Peterborough soon found their feet and went ahead in the 16th minute when Tommy Williams' floated cross was glanced in by Mclean.
With their tails up, Posh began producing the slick football which has been a trademark of their successive promotions.
Rangers would surely have been two down had debutant Ben Watson not put in a superbly-timed challenge to rob Lee Frecklington as the midfielder raced through.
And Watson's last-gasp intervention proved pivotal moments later when the hosts hauled themselves level.
Simpson was played in by Taarabt and reached the byline before cutting the ball back to Routledge for a simple finish.
Watson could have marked his debut with a goal just before the hour when a loose ball found him in the area but could only sidefoot his effort wide.
Magilton removed Taarabt and ineffectual £3.5million Argentinian Alejandro Faurlin, replacing them with Championship-hardened campaigners Rowan Vine and Martin Rowlands.
But Posh continued to threaten and Toumani Diagouraga forced Radek Cerny into a smart save with a fierce 25-yard drive before Damion Stewart deflected Tommy Rowe's shot over.
Simpson could have won it for Rangers with five minutes remaining but hurriedly blasted his shot high and wide.
But Magilton was a relieved man at the death when an offside flag denied Mackail-Smith a winner.