Daniel Candeias' second dismissal in four appearances swung the initiative towards the LaLiga side on half-time, but Steven Gerrard's men were largely comfortable in securing a precious point.
The result, aided by Allan McGregor's vintage performance, means Rangers will reach the knockout rounds if they win away to second-placed Rapid Vienna on the final matchday on December 13.
Group G leaders Villarreal, who are still to host Spartak Moscow, were left to rue a missed opportunity to confirm their progression with all four teams now split by two points.
What a save from McGregor in the first half to deny Ekambi. pic.twitter.com/FPuZZx3SKe— Rangers Football Club (@RangersFC) November 29, 2018
The game's earliest opportunity fell kindly to Scott Arfield, but the midfielder - a scorer in the 2-2 draw in the reverse encounter - stabbed straight at Andres Fernandez.
Connor Goldson sliced over at close range on the half-hour and was let off for keeping Karl Toko Ekambi onside at the other end, McGregor off his line to smother in a one-on-one.
The Scotland goalkeeper again denied the influential Toko Ekambi moments before Candeias, booked for a late tackle in the 36th minute, was shown a second yellow late in the half after appearing to tread on Santiago Caseres.
Gerrard was furious with the circumstances that saw his Portuguese winger dismissed at St Mirren earlier this month, but his mood here will have been lifted by the resilience that followed.
Ramiro Funes Mori volleyed across the face in the dying moments of normal time in one of few Rangers scares on the way to a crucial clean sheet.
50,171 inside Ibrox Stadium this evening. pic.twitter.com/f1gX2q9A7f— Rangers Football Club (@RangersFC) November 29, 2018