The Magpies were without striker Shola Ameobi due to injury, with deadline day signing Sibierski handed his first outing since his switch from Manchester City.
The Frenchman, playing just behind Obafemi Martins, made a perfect start to his career for United and after missing an early chance broke the deadlock just ten minutes in.
Sibierski met a Damien Duff free-kick from the right at the back post and his deflected headed effort left goalkeeper Artur Kotenko with no chance.
The home side threatened an equaliser just before the half-hour mark, as Marek Lemsalu got clear at the far post to meet Konstantin Nahk's long ball forward, but his effort drifted just over.
Soon after Newcastle had to make a reshuffle as centre-half Titus Bramble had to leave the field, with midfielder James Milner taking his place.
As half-time approached the Magpies began to re-assert their authority, with Martins' pace causing problems.
Early in the second half Shay Given was forced into a smart block from Vladimir Voskoboinikov's stinging drive, before Konstantin Vassiljev lashed the rebound over the crossbar from 12 yards.
Martins made space for a shot on the hour, but fired well over the top from 20 yards out.
The latter stages of the game saw Newcastle content to keep a lid on things and ensure that Levadia didn't forge any chances to grab an equaliser.
Martins flashed a last-minute effort a yard wide of Kotenko's left-hand post as Glenn Roeder's side got the job done in Estonia.