Back-to-back defeats to St Johnstone and Kilmarnock had piled the pressure on Graeme Murty but his charges put in a much-improved performance at Ibrox.
The hosts went on to open the scoring on 50 minutes when a corner kick fell to Danny Wilson inside the penalty area and the 26-year-old rifled home from a right angle.
Gers then doubled their lead on 76 minutes through Morelos, who converted from inside the penalty area after beating the offside trap on his way through on goal.
The result sees Gers consolidate their hold on third place, while Motherwell are eighth in the standings.
Rangers (4-1-2-1-2): Foderingham; Tavernier, Alves, Wilson, John; McCrorie; Jack (Barjonas 41'), Holt; Kranjcar (Pena 83'); Morelos (Hardie 84'), Herrera
Motherwell (3-5-2): Carson; Kipre, Hartley, Dunne; Tait, Bigirimana, McHugh (Campbell 20'), Grimshaw, Rose (Bowman 62'); Fisher (Newell 78'), Tanner