Kris Boyd volleyed Rangers into an early lead before Merouane Zemmama twice came close for the visitors.
BBC: Kris Boyd scores for Rangers
2.
Substitute Merouane Zemmama's free-kick was deflected wide of the Motherwell goal and, from the resulting corner, Chris Hogg's header was claimed by Ruddy.
BBC: Motherwell striker Jamie Murphy
3.
Home substitute Byrne, on for early injury victim Merouane Zemmama, did get a glimpse of goal after some impressive work from Anthony Stokes.
BBC: SPORT | Football | Scottish Premier | Hibernian 2-0 Aberdeen