Boro were depleted from the 43rd minute when goalkeeper Jason Steele sprinted outside his penalty area and brought down Leeds striker Dexter Blackstock with a clumsy lunge.
Steele angrily challenged the decision in vain and Karanka immediately sent on Basel-born keeper Jayson Leutwiler, sacrificing Marvin Emnes.
A bumper crowd of over 30,000 saw Ross McCormack head Leeds into a 35th-minute lead with his seventh goal in three games and, although Mustapha Carayol equalised on 52 minutes, defender Jason Pearce nodded Leeds back in front five minutes later.
Karanka, the former defender at Real Madrid, where he spent three years as Jose Mourinho's assistant, described his arrival at Middlesbrough as a new era and a fresh start.
Although his players had an extra spring in their step as they sought to impress their new boss they gave Leeds keeper Paddy Kenny too little work.
Boro were fortunate not to concede a 21st-minute penalty when Daniel Ayala's handling offence to divert the ball away from the lurking McCormack was adjudged by referee Philip Gibbs to be just outside the box, much to McCormack's disgust.
Ayala escaped with a yellow card and Leeds failed to make the resultant free-kick count. McCormack had another penalty claim waved aside immediately afterwards when Marvin Emnes shoulder-charged him inside the box.
McCormack's response was to trick former Leeds and England defender Jonathan Woodgate on the right and cross for Blackstock to balloon over the bar from eight yards.
Livewire McCormack then created space for Danny Pugh whose drive was turned away for a corner by Steele.
McCormack's frustration finally ended when he put Leeds in front with his 13th goal of the season.
Tom Lees rose above Boro's defence to nod Luke Murphy's corner back across goal for the Scot to head in at point-blank range.
Steele's controversial departure left Boro a massive task but they equalised seven minutes after the break.
Albert Adomah's superb through ball split Leeds' defence wide open and Carayol swept a first time shot past Kenny.
Leutwiler pulled off a superb diving save from Alex Mowatt but Leeds were back in front when skipper Rudolph Austin's cross from the right was headed in at the far post by Pearce.
Karanka surprisingly replaced scorer Carayol with former Darlington striker Curtis Main 23 minutes from the end and as Leeds looked for a third goal, Mowatt again went close and Austin headed just outside a post.
Karanka must have been pleased with his side's spirit but they carried too little threat in attack.