The Hoops trailed at half-time to Stefan Nikolic's strike but goals early in the second period from Georgios Samaras and Mohamed Bangura earned victory for a team overseen by assistant manager Johan Mjallby.
Bangura had an early effort blocked after chesting down Adam Matthews' excellent cross, moments after a mix-up between Thomas Rogne and goalkeeper Lukasz Zaluska almost let in Steaua for an opener.
The Romanian side took the lead in the 13th minute, though, when Adrian Popa set up Montenegro forward Nikolic to finish powerfully past Zaluska from the edge of the penalty area.
Rogne blocked Alexandru Chipciu's goalbound effort and Popa hammered in a fierce shot which crashed off the crossbar and out of the ground.
Rusescu went close early in the second half but within minutes, Celtic were 2-1 up.
One substitute, Samaras, equalised before another, Kris Commons, provided the cross for Bangura to superbly head the Scots in front.
Zaluska saved sharply to prevent Iasmin Latovlevici's deflected cross flashing inside the near post and also denied Adi Rocha, while Nouioui Lassad missed a good chance for Celtic after Charlie Mulgrew's free-kick was fumbled.