Morrison, who joined from West Ham in mid-February, struck in the 14th and 73rd minutes to allow Rangers to take advantage of slip-ups by their promotion-chasing rivals.
With the top two not playing, none of the other teams in the top 12 in action managed a win with Derby and Nottingham Forest slipping to surprise defeats at home to Millwall and away to Barnsley respectively.
Steve Morison, the on-loan Leeds forward, scored the only goal in the 61st minute to end Derby's seven-match unbeaten run.
Dale Jennings was Barnsley's hero with the solitary goal in the 51st minute to move his side off the bottom of the table.
Yeovil's 2-0 win at home to Sheffield Wednesday, meanwhile, put them within two points of safety.
Ishmael Miller scored twice in the 10 minutes either side of half-time, with the Owls' misery completed by Sam Hutchinson's late red card.
Wigan's involvement in the FA Cup allowed Reading to creep back into the last play-off place, albeit on goal difference, with a 1-1 draw at Brighton.
Trailing to Chris Gunter's 17th-minute own goal, the Royals capitalised on the sending-off of Gordon Greer - with Royston Drenthe equalising just past the hour.
Bolton stunned Leeds with a 5-1 victory at Elland Road, easing their relegation worries.
Joe Mason's effort on the stroke of half-time was followed by goals from Lukas Jutkiewicz, Zat Knight, Mark Davies and Andre Moritz before Matt Smith's last-minute consolation.
Doncaster ensured they kept themselves clear of the relegation zone with a 2-0 win at home to Huddersfield thanks to goals from Billy Sharp and David Cotterill.
On-loan striker Danny Graham opened his account for Middlesbrough with both goals in the 2-0 win at home to Ipswich.
The Sunderland forward, in his second loan spell of the season after a miserable spell at Hull, grabbed both his goals in the latter stages of the first half.
Bournemouth moved closer to mid-table security as Lewis Grabban's penalty early in the second half ensured Blackpool still have to worry about their proximity to the bottom three.