Luke Murphy’s speculative effort from long distance appeared to deceive home goalkeeper Adam Federici and gave Leeds the lead midway through the second half. Sam Byram then sealed the win in the last minute when nodding in unmarked at the far post.
Leeds have stuttered all season and the permanent appointment of manager Neil Redfearn in November had not seemed to have improved matters.
Prior to the visit to the Madejski Stadium, Redfearn had overseen just four wins in his 15 matches in charge.
Neither of the teams were able to muster any worthwhile attempts on goal in the lacklustre opening exchanges.
Reading did most of the pressing, mainly through the right-wing runs of Garath McCleary, but could not produce any end product.
Pavel Pogrebnyak also tried to pierce the Leeds defensive cover but was thwarted by an excellent tackle from Tommaso Bianchi.
Leeds replied through Steve Morison but his low cross from the byline was scrambled clear by Federici and his defenders.
Bianchi tested Federici soon after with a firm drive but played little further part. He injured a knee in a collision with Danny Williams and was replaced by Casper Sloth on the half hour.
Lewis Cook broke clear and found Morison but the striker’s low effort struck Federici’s left-hand post and bounced to safety.
After a poor first half from both sides, Reading set about making amends after the interval. Stephen Kelly crossed from the right but Blackman’s header was weak and carried little danger for Leeds goalkeeper Marco Silvestri.
It was against the run of play, though, when Leeds went ahead in the 63rd minute.
There appeared little threat when Murphy gathered the ball 35 yards out but he unleashed a fierce drive that Federici seemed to see late and could only help on its way into the net. Byram sealed a much-needed Leeds victory in the 90th minute when nodding in from Morison’s far-post cross.
Reading: Federici, S Kelly, Hector, Pearce, Obita, Williams, Norwood (Mackie 64), Chalobah, McCleary, Pogrebnyak (Cox 71), Blackman (Yakubu 71). Unused substitutes: Robson-Kanu, Akpan, Andersen, Cooper.
Leeds: Silvestri, Wootton, Bamba, Bellusci, C Taylor, Murphy, Bianchi (Sloth 30), Byram, Cook, Mowatt, Morison. Unused substitutes: Sharp, Cani, S Taylor, Doukara, Antenucci, Del Fabro.
Referee: G Scott (Oxfordshire).