McCoist, who inherited the job from Walter Smith at the end of last season, endured three defeats on the recent pre-season tour of Germany but will have been buoyed by a strong showing in Belfast.
A strong Rangers starting XI, including Northern Ireland internationals Steven Davis and David Healy on familiar territory, started well and scored the first goal of the McCoist era after 20 minutes.
New signing Juan Manuel Ortiz was scorer, cutting inside the defence before sending the ball past Alan Blayney in the home goal.
The equaliser came in unusual fashion, Davis' shot rebounding a long way down the field where Michael Carvill collected before lashing past Allan McGregor.
With 67 minutes gone Healy played in Steven Naismith, who made it 2-1 with a neat finish.
Rangers' third came after good build-up play between Naismith and Kane Hemmings, who combined to leave Nikica Jelavic with a simple finish.
Hemmings went from creator to scorer six minutes from time when he picked up a Sasa Papac pass and finished well.