Robert Snodgrass was the man to bring Warnock his first goal since he succeeded Simon Grayson in February, dragging the ball underneath Boro keeper Jason Steele in the 18th minute.
Luciano Becchio made it two just nine minutes later following a dreadful mistake by Justin Hoyte. Barry Robson's late dismissal in a tussle with Adam Clayton added insult to injury for Boro.
Despite a much-improved performance in the second half, Tony Mowbray's men were unable to overcome the two-goal deficit and reduce the gap on the automatic promotion places.
Warnock's Leeds, however, remain in 10th place but are now within four points of making a late surge for the play-off places.
A period of applause in tribute to Middlesbrough's long-serving recruitment co-ordinator Jack Watson, who passed away aged 90 yesterday morning, preceded kick-off.
Becchio glanced a header across the box only for Ross McCormack to skew wide under as the visitors poured on the early pressure.
Nicky Bailey drove aimlessly over Andy Lonergan's bar as Leeds sat deep, content to restrict their hosts to speculative efforts.
Lukas Jutkiewicz and Darren O'Dea then clashed heads, the latter coming off worse, and as the action resumed Marvin Emnes bustled into space to clip a promising strike into the away fans.
But the Dutchman's verve failed to inspire Boro and they soon fell behind.
In the 18th minute, O'Dea sprayed a perfectly-weighted ball down the right flank for Aidan White. The Leeds-born winger dragged the ball across to the waiting Snodgrass, who slotted underneath Steele to register a first Leeds goal under Warnock's stewardship.
And less than 10 minutes after drawing first blood, Leeds doubled their lead.
Hoyte failed dismally to clear a Becchio through-ball, allowing its intended recipient McCormack to claim ownership and turn the ball across the goalmouth for the Argentinian to coolly convert from six yards.
Robson forced Lonergan to punch behind as Boro pressed to gain a foothold in the game, but it might have been three to the visitors at the break if Becchio had coped better with a glorious long ball into Steele's box.
The Leeds offensive showed no signs of abating as the second half got under way, with Snodgrass quick to ripple the side netting with a fearsome drive that the away fans thought had beaten Steele.
Mowbray had opted to make no substitutions during the interval, but his side's renewed vigour soon showed. Rhys Williams angled a bullet header just wide of a post as Robson lofted a fine free-kick across the goalmouth.
Boro's momentum was interrupted, though, as Williams pulled up following a clash with Becchio, and Leeds took advantage to test Steele once more.
Clayton picked his spot, his dipping drive nicking off Matthew Bates to nestle on the top of the net with the home stopper flat-footed.
The struggling Williams was withdrawn as part of a double substitution after the hour mark, Jutkiewicz also removed as Kevin Thomson and Curtis Main took to the field.
A period of quiet tension preceding the final 20 minutes was only punctuated by a blazing drive beyond the near post from the eager Clayton.
McCormack was just shy of dancing on to a White back-heel in the 73rd minute as Leeds sought to put the game to bed.
But the result was surely beyond Middlesbrough as recent substitute Thomson took a kick to the head, to be replaced by Bart Ogbeche.
And in a final blow to Boro's chances of a late recovery, Robson was shown a straight red card for raising his hands to Clayton as time ticked away at the Riverside.
Leeds rode out the seven minutes of injury time to claim a valuable victory and delight the near 3,000 travelling fans.