A farcical goal by Atsuto Uchida when his cross floated into the net put Schalke ahead in the 67th minute, triggering a transformation in the hosts.
Well-crafted goals by Kevin-Prince Boateng and Julian Draxler in the 78th and 85th minutes gave Schalke what looks like an easy victory but until Uchida's opener they were disjointed, squandering possession and chances.
A poor clearance by the visitors saw the ball loop to Adam Szalai which the striker controlled on his chest before a left-right combination ended with a shot goalkeeper Ciprian Tatarusanu had to be smart to get down to.
Boateng drew a reaction save from Tatarusanu after he rose at the far post and headed Adam Szalai's cross goalwards with the keeper parrying the ball for a corner.
Steaua then came within inches of taking the lead when Cristian Tanase's shot from distance was tipped round the post by Timo Hildebrand although the ball came at the keeper at a good height.
The hosts enjoyed a flurry towards the end of the first half. Jefferson Farfan controlled the ball in his own half and released Boateng who ran on into the area but he delayed releasing the ball and it was deflected out.
From the resulting corner Boateng drilled the ball goalwards but it came off a Steaua defender and went just past the post.
Steaua attacked in the opening seconds of the second half, and Alexandru Bourceanu's corner was just behind Pantelis Kapetanos with the striker only able to hook the ball over.
The visitors again reminded Schalke they possessed a threat when Alexandru Bourceanu's header was cleared off the line by Uchida with the ball eventually coming to Kapetanos who curled wide.
Steaua's Adrian Popa showed clever feet on the right of the area close to the byline but his cross was smashed rather than placed and it went across the face of goal.
The crowd were getting restless but Schalke went ahead out of nowhere and fittingly there was an element of farce.
Uchida floated in a cross from the right which eluded everyone including the goalkeeper who was rooted to the spot, looking on in horror as the ball bounced and went into the net.
However, there was no fluke in Schalke's second goal as Farfan drove forward, slid the ball across for Draxler at the edge of the area and he in turn touched the ball through to Boateng who sent a side-footed shot across the goalkeeper and into the bottom right-hand corner.
Draxler started and finished a move which saw him run on to Christian Fuch's inch-perfect throughball and dink the ball over the keeper for Schalke's third.
Christian Clemens hit the post in injury time for the hosts.