Stuart Dallas netted the winner and Bailey Peacock-Farrell saved a last-gasp penalty as Leeds kept the pressure on Sky Bet Championship leaders Norwich with a 1-0 victory over struggling Reading at Elland Road.
Similar to against Bristol City on Saturday, United improved after the interval and the Royals finally buckled under the constant pressure when Dallas struck on the hour mark.
Dallas' Northern Ireland team-mate Peacock-Farrell then took centre stage in a dramatic finale, securing back-to-back wins by saving Marc McNulty's penalty.
Marcelo Bielsa's side leapfrogged Middlesbrough into second place in the table, moving one point behind Norwich, ahead of Saturday's trip to fellow high-flyers Sheffield United.
The defeat turned up the heat on Reading manager Paul Clement. The Royals remain above the relegation zone on goal difference alone following a run of one win in six matches.
Leeds came out firing and had a glorious early chance when Pablo Hernandez found Barry Douglas unmarked at the back post, yet the defender somehow headed wide.
Reading midfielder Leandro Bacuna almost caught Peacock-Farrell off his line from a 30-yard free-kick, with the fit-again goalkeeper managing to scramble back and tip the audacious effort over.
Shortly after in the 11th minute, chants of "Oh, Gary, Gary" rang around the ground to mark the seven-year anniversary of former Leeds midfielder Gary Speed's death.
The crowd were nearly on their feet again as the in-form Kemar Roofe had an acrobatic volley blocked, glanced a header wide and then curled an effort from distance over the crossbar.
As the hosts slipped off their early standards, Reading came into the game and occasionally offered a threat on the break.
Bielsa made a double substitution at half-time, injecting more pace and creativity into the hosts with the introductions of Samuel Saiz and Jack Clarke for Gjanni Alioski and Lewis Baker.
And the changes almost immediately paid off as Saiz's shot from Clarke's cutback was deflected wide by Andy Yiadom for a corner, from which Liam Cooper headed tamely at Anssi Jaakkola.
The Reading goalkeeper kept his side in the game in the 56th minute with a stunning low save to his right after Roofe met a sublime curling Douglas cross.
But Leeds' pressure finally paid off four minutes later as Dallas, having seen a sprawling Roofe denied, converted from close range following fine work down the left by Hernandez and Douglas.
United were determined to secure that crucial second goal, with Hernandez scuffing a shot wide and Jaakkola keeping out Roofe from close range late on.
They were almost punished when Douglas brought down Sims in the area, but Peacock-Farrell produced a one-handed save down to his right to deny the substitute from the spot.
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