Coventry hit back, although they ended the match with 10 men after skipper Stephen Wright was sent off for a second bookable offence following a late foul on Buzsaky.
Chris Coleman's side went ahead in the 16th minute, when Best beat R's defender Matt Connolly to Patrick van Aanholt's free-kick and sent a looping header beyond keeper Radek Cerny.
Van Aanholt had almost scored four minutes earlier. The on-loan Chelsea left-back played a neat one-two with Clinton Morrison before seeing his low shot excellently tipped away by Cerny.
Ben Watson had a chance to equalise for Rangers after a similar exchange of passes with Wayne Routledge, but the midfielder fired wide.
Rangers thought they had levelled when Buzsaky threaded the ball through for Simpson, who slotted into the net but was adjudged to be offside.
But Simpson beat the offside trap ten minutes before half-time, latching on to Alejandro Faurlin's chipped pass to nudge the ball past keeper Kieran Westwood.
Rangers stepped up a gear in the second half and Adel Taarabt twice came close to putting them in front.
Taarabt hit the bar with a delightful chip from just outside the penalty area and then shot inches wide after riding two challenges.
The breakthrough for Rangers came when the visitors struggled to clear Faurlin's corner and the ball eventually dropped to Buzsaky, whose left-footed drive went in via a deflection off Wood.
But Wood, recently signed from Sheffield Wednesday, had the last laugh by heading home Michael McIndoe's right-wing free-kick.
Coventry then had to hang on after the dismissal of Wright, who angrily threw his captain's armband towards referee Mike Jones after being given his marching orders.