Leon Best headed his ninth goal of the season to put Coventry ahead before Jay Simpson pulled the hosts level shortly after the half-hour mark with a neat finish.
Adel Taarabt was a constant menace all afternoon for the Hoops and Akos Buzsaky deservedly fired them ahead in the 69th minute before Wood's late leveller.
A lively clash threw up more incident six minutes from time when Sky Blues captain Stephen Wright was dismissed for a second bookable offence, after which he appeared to throw his captain's armband at referee Mike Jones.
The result meant Coventry have now gone eight games without victory, although they will be much happier with a point than a QPR side who hardly banished the memory of last weekend's 2-0 defeat at Doncaster.
Both sides enjoyed a positive start to the encounter, with Taarabt firing a shot come cross along the face of goal after just three minutes.
Hoops keeper Radek Cerny was called upon to keep out Patrick Van Aanholt's goalbound effort with a superb diving save soon after, before the hosts broke and threatened again themselves through Wayne Routledge.
It was no real surprise when the opening goal came with just 16 minutes on the clock and it was the visitors who grabbed the initiative.
Best earlier this week insisted Coventry would be a different team if they could start games in the same way they finish them, having gone behind on four occasions during their winless streak.
And it was he who put them ahead by sending a looping header over the stranded Cerny from Van Aanholt's free-kick.
Rangers immediately hit back and the lively Taarabt was giving Wright all sorts of problems down the left wing, while also forcing a solid save from Keiren Westwood.
The complexion of the first half changed completely within the space of 60 seconds when Best headed a great chance wide when all he had to do was hit the target.
And from almost being 2-0 down, QPR were level when Simpson latched onto Alejandro Faurlin's through-ball to fire past Westwood.
Aron Gunnarsson then saw his stoppage-time header cleared off the line by Matthew Connolly as a thrilling first half ended level.
The ambition of both teams remained evident after the break as they created openings in search of a second goal.
First Taarabt was unlucky to see his deft chip hit the crossbar after a superb bit of skill, before Van Aanholt put in a great recovering tackle to deny Routledge as he looked to pull the trigger.
The hosts were soon starting the dominate things once again with Faurlin and Ben Watson going close and they got the breakthrough they deserved in the 69th minute.
With the Sky Blues becoming camped in their own half, a Hoops corner remained in the danger zone and Buzsaky's drilled shot from close range took a deflection before beating Westwood.
Gunnarsson saw his effort deflected over the bar as Coventry, aided by some attacking substitutions, pressed in search of an equaliser.
And they got it through Wood before fellow defender Wright saw red.