The result now means that the Light Blues will need to win all of their remaining games to secure the championship.
Manager Walter Smith made three changes from Florence with Christian Dailly, Nacho Novo and Daniel Cousin replacing Brahim Hemdani, Steven Whittaker and Jean-Claude Darcheville.
The game took a long time to warm up, with the respective midfields holding sway.
Indeed it took until the 36th minutes for either goalkeeper to be tested - Andy McNeil clawing out a Carlos Cuellar header from a Steve Davis cross.
Four minutes later a Davis - Kirk Broadfoot move down the right saw the full-back's cutback find Novo whose shot was deflected wide by Rob Jones.
The first yellow card of the afternoon fell to Cuellar for a foul on Steven Fletcher - a booking that will see the Spaniard suspended for the St. Mirren game on 19 May.
Rangers restarted on the offensive, Cousin's twenty-yard left-foot shot from a Davis lay-off whistling inches over the bar in 51 minutes.
Two minutes later missiles were thrown at Kevin Thomson from the home support as the Ranger prepared to take a free-kick - Referee Calum Murray clearing the objects off the pitch himself, before the midfielder saw his cross headed goalwards by Dailly and into the net by Cousin, only to be ruled out for offside by linesman Lawrence Kerrigan.
The visitors were piling on the pressure at this juncture - Barry Ferguson's angled drive from a Davis pass being blocked by McNeil in 56 minutes.
Five minutes later - at the other end - Neil Alexander produced a fine one-handed save to deny Filipe Morais' twenty-yard drive from a John Rankin pass.
Alexander again proved equal to the task on seventy minutes, holding Fletcher's 25-yard shot.
Kris Boyd replaced Sasa Papac six minutes later, and almost immediately Thomson was inches wide with a 22-yard free-kick.
Darcheville substituted for Cousin in 84 minutes - but time was running out for the Ibrox men.
The final chance of the game came four minutes later when a long, deep Dailly free-kick was headed over by Cuellar.
The game ended goalless - and afterwards a disappointed Walter Smith reflected:
"I'm disappointed not to win. Both sides were slow to start. We took time to impose ourselves, but finished the stronger. We now have to win all our remaining games."
On the subject of the UEFA Cup Final, Smith had a blast at the SPL:
"There's no willingness on anyone's part to help us prepare for the final."
HIBERNIAN McNeil; McCann, Canning, Jones, Chisholm; Morais (O'Brien 83), Shiels, Murray, Rankin; Campbell (Donaldson 74), Fletcher UNUSED SUBS Ma-Kalambay, Kerr, Benjelloun, Zarabi, Stevenson
RANGERS Alexander, Broadfoot, Cuellar, Weir, Papac (Boyd 76); Davis, Ferguson, Dailly, Thomson, Novo; Cousin (Darcheville 84) UNUSED SUBS G. Smith, Faye, Lennon, Elmslie, Loy
REFEREE Calum Murray