Marcelo Bielsa suffered his first defeat as Leeds boss in the EFL Cup defeat to Preston North End during the week, and the Whites looked sluggish during this encounter, too, with Boro nullifying its host's attacking threat.
The visitors should have gone ahead in the 24th minute, only for Britt Assombalonga to direct a free header wide from a corner, although Leeds was fortunate that Liam Cooper's foul on Aden Flint at the same set-piece was not spotted by referee Tim Robinson.
Boro's resolve was tested soon after as Leeds carved out a rare opportunity, but Adam Clayton reacted sharply to hook Luke Ayling's glancing header off the line.
Clayton was in the thick of the action again after the restart - Barry Douglas lucky to escape with just a booking for a reckless, over-the-top challenge on the former Leeds midfielder, while Assombalonga had another penalty claim turned down.
Daniel Ayala netted a late winner against West Bromwich Albion last time out, but the Spaniard could not repeat that feat this time, heading wide from Muhamed Besic's free-kick before drawing an instinctive save out of Bailey Peacock-Farrell as Leeds's winning run at home under Bielsa in the league came to an end.