Record club buy Massimo Maccarone was the matchwinner with two goals in the closing stages.
Boro made hard work of their success before a crowd of 9,436, the lowest for a European game at The Riverside in two seasons.
Middlesbrough manager Steve McClaren stuck to his pre-match promise of giving youth a chance. Four teenagers - James Morrison, Matthew Bates, Jason Kennedy and Adam Johnson - were in the starting line-up.
Jimmy Floyd Hasselbaink captained the side with regular skipper Gareth Southgate rested for the Premier League home game with Spurs on Sunday.
Boro began in lively style and looked as though they would establish command in the early stages. They failed to capitalise on their pressure and the visitors came more into the game as half-time approached.
Give credit to a hardy bunch of flag-waving, drum-beating visiting supporters who had spent three days in a coach travelling from Bulgaria to Teesside. The 36-strong party certainly offered noisy support.
The visitors could have snatched the lead when Mihail Venkov provided a pass from the left for Milivoije Novakovic to run on to and hit a tremendous shot just wide.
Morrison was lively in the Middlesbrough side. He looked the most promising of the academy youngsters and could have won a penalty when he had fell to the ground after breaking through.
Middlesbrough were awarded a free-kick on the edge of the penalty area shortly after the break but they wasted it.
Novakovic hit a brilliant shot on the turn for the visitors that was well saved by Australian Under-21s international goalkeeper Brad Jones.
Litex gained in confidence as the game wore on but Boro finally broke the deadlock through Maccarone ten minutes from time.
Johnson provided a left-wing cross to the far post where Maccarone scored with a header in the six-yard box.
The goal lifted the Italian striker and he followed up with a brilliant second goal when he blasted a 20-yard shot into the roof of the net that left the goalkeeper completely helpless.
Boro introduced substitute Lee Cattermole seven minutes from time, which meant they finished the game with five teenagers in their side.
However, Cattermole caught the attention of the match referee after coming on and was booked for a foul.