Rangers are without defenders Madjid Bougherra and Andy Webster, while midfielder Maurice Edu and strikers James Beattie and Nikica Jelavic are all still missing.
It was a cross that Everton striker Nikica Jelavic would have craved and it was probably that realization that prompted Slaven Bilic to introduce the striker midway through the second half.
Nikica Jelavic scored the only goal of the game and it could have been worse for Villa with Christopher Drazan having a shot cleared off the line for the dominant hosts.
Even so, goals from midfielder Leon Osman and substitute Nikica Jelavic kept David Moyes' team in sixth place, three points ahead of city rivals Liverpool with a game in hand as the club's manager celebrated 11 years in charge.
Calderwood's side gifted Motherwell two goals from set-pieces at the weekend and were guilty of a further defensive lapse against Rangers when Richie Towell, making his debut, played a terrible back-pass that allowed Nikica Jelavic to run through and score.