They took over at the summit on goal difference from Burnley, who were held to yet another goalless draw - their 12th of the season - by Derby on Tuesday (Wednesday AEDT).
On a night of more twists and turns, the third side in the automatic promotion chase, Sheffield United, slipped to third after a 1-0 home loss to Millwall.
Dan James' second-minute strike proved decisive for Leeds at the Riverside Stadium as Daniel Farke's side leapt from third to reclaim control of the title race.
Play-off hopefuls Boro pushed for a late equaliser but Leeds, much to their relief after having two goals harshly ruled out for offside, held on.
Burnley endured more frustration in their stalemate at Pride Park and they needed a good save from James Trafford to prevent Jerry Yates winning it for the Rams, who remain just above the relegation zone.
The Blades slipped to a second successive defeat as Millwall's Josh Coburn scored the only goal at Bramall Lane.
Fourth-placed Sunderland claimed the point they needed to ensure at least a play-off place with a 0-0 draw at Norwich, while Bristol City tightened their grip on a top-six spot with a last-gasp 2-1 win over West Brom.
Haydon Roberts scored the Robins' winner at Ashton Gate in the sixth minute of stoppage time as play-off rivals Albion were made to pay for the late sending-off of Jayson Molumby.
Nahki Wells and Alex Mowatt had earlier traded goals.
At the bottom end of the table, Cardiff's Yakou Meite scored a vital late equaliser as Cardiff snatched a 2-2 draw at Preston.
Fellow strugglers Luton also claimed a dramatic late point as Millenic Alli rescued a 1-1 draw at Stoke, who had led through a deflected Lewis Baker free kick.
Blackburn recovered from 0-2 down at halftime to draw 2-2 with Sheffield Wednesday at Ewood Park.
Moussa Sissoko scored the only goal as Watford beat Hull 1-0.
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