The stuttering pre-season promotion favourites fell behind to Ross McCormack's 24th goal of the season on 14 minutes after the Leeds striker had earlier missed a penalty.
But midfielder Jenas ensured QPR avoided a fourth straight defeat when he slotted in the equaliser just before half-time.
Under-pressure Rangers manager Harry Redknapp came out fighting this week, denying suggestions his position is under threat while claiming their recent form is nothing more than a 'blip'.
However, that blip was in danger of turning into a full-blown crisis when McCormack fired Leeds ahead with a deflected free-kick, just moments after he had missed a penalty.
The visitors were gifted the chance to take a 10th-minute lead when Richard Dunne's clumsy challenge sent McCormack tumbling in the penalty area.
But McCormack's spot-kick was a weak effort which Rob Green saved low to his left.
However, the in-form frontman made amends four minutes later, from about 10 yards further out, with a curling free-kick which clipped the Rangers wall on its way past Green.
Leeds, themselves looking to climb into the play-off picture, could have doubled their lead but Green denied Cameron Stewart and Connor Wickham, on his debut following his loan switch from Sunderland, fired wide.
Rangers looked woefully short of ideas for the majority of the first half and a Jenas header which looped straight into the arms of goalkeeper Jack Butland was the sum total of their efforts, until a minute before the break.
And it was Jenas who hauled them level when he collected Kevin Doyle's lay-off from Ravel Morrison's pass and dispatched it past Butland from the edge of the area.
The goal briefly sparked Rangers into life when they came out for the second half and Armand Traore's shot was well turned behind by Butland.
Leeds twice came close to regaining the lead through Wickham, who was inches away from a debut goal when his shot flew across Green and narrowly wide of the far post.
Then a minute before the end Wickham had a free header in the Rangers penalty area only to plant it straight at Green.
But there was drama in stoppage time when Rangers defender Clint Hill thought be had snatched an unlikely winner only to be flagged offside.