It was a point Palace hardly deserved as they created very little against a much better Rangers side.
But Luigi De Canio's outfit have only themselves to blame as they missed three clear chances to rack up three points after on-loan Scott Sinclair had given Rangers the lead on the stroke of half-time.
Palace just couldn't get going and Jose Miguel Fonte's header over the bar was all they could muster in a lack-lustre first half.
Rangers more than edged the first period and it came as no surprise when Sinclair headed the West Londoners in front on 45 minutes.
Palace failed to clear Martin Rowlands' corner, despite three attempts, and Akos Buzsaky's cross found Sinclair who beat Julian Speroni with a well-placed glancing header.
After the break Rangers had chances to complete a convincing win. Buzsaky's precise pass left Sinclair one-on-one with Speroni, but the Argentinian keeper saved well. A few minutes later Buzsaky was the supply line again but this time skipper Adam Bolder missed a good chance.
Rowan Vine was then added to the offenders list as Speroni completed a hat-trick of saves.
Rangers were heading for their fourth win in seven matches until, with two minutes left, Mark Kennedy's free-kick dropped perfectly to Morrison who headed firmly past Lee Camp for an unlikely point.