Mark Viduka returned to partner Jimmy Floyd Hasselbaink in attack, while Brad Jones continued in goal in place of the injured Mark Schwarzer, as Boro looked to turn around a one-goal deficit from the first leg.
However, Steaua had the first chance as first-leg goalscorer Nicolae Dica headed over from ten yards out at the near post following a third minute corner.
Sixteen minutes in Steaua made a crucial breakthrough as Jones spilled a long-range effort from Petre Marin and Dica was on hand to tuck home the rebound from eight yards.
Eight minutes later Steaua led 2-0 on the night and 3-0 on aggregate as centre-back Dorin Goian saw his initial header blocked following a corner, before he rammed in the rebound.
Boro had to take off the injured Gareth Southgate soon after and his replacement, Massimo Maccarone, threw Steve McClaren's side a lifeline 12 minutes before the break by netting from Viduka's measured pass.
Viduka almost levelled on the night twice before the break, but was denied on both occasions by Steaua's Portuguese goalkeeper Carlos.
Ten minutes after the restart Boro threw on Yakubu for Andrew Taylor as they were forced to go for broke with three strikers.
That move paid off just past the hour mark, as Stewart Downing swung the ball in from the left and Viduka headed home over the stranded Carlos.
Nine minutes later it was game on at 3-2 on the night as Carlos could only parry Downing's low shot and Chris Riggott bundled in the rebound from close in.
The pressure was all on Steaua now and they cracked in the final minute of normal time as Maccarone was in the right place to head home a perfect far-post cross from the impressive Downing.
The Italian was the hero, as he had been against Basel, with the final whistle sparking celebrations all around the ground as Boro clinched a place in their first-ever European final on another astonishing night at The Riverside.