The draw, and Basel's 1-0 win over group leaders Chelsea, means Schalke slipped to third in the group and have it all to do in their final pool game which is a winner-takes-all tie against the Swiss side on December 11.
Romanian champions Steaua have been in impressive form this season despite being bottom of the group, as they are are undefeated in the league and have qualified for the Romanian Cup quarter-finals for the first time since winning the competition in 2010/11.
That form showed in Bucharest as they kept the German visitors at bay, although their late efforts to snatch a win and keep their hopes of progression alive were extinguished by the visitors.
Schalke midfielder Jermaine Jones had an effort on goal in the 24th minute in the first real chance of the match as the German side looked to assert themselves and were seeing most of the ball.
Five minutes later, Jefferson Farfan missed the target when he attempted a first-time volley after the ball was whipped in from the left, however, the Peru international was unable to find any control and instead blazed it over the crossbar.
Schalke goalkeeper Ralf Fahrmann was then called into action for the first time in the game when Steaua striker Federico Piovaccari was picked out at the the back post. Fahrmann was directly in line and made a good save as the forward tried to volley the ball past him from a tight angle.
The visitors, however, were on top as the game approached half-time despite being unable to find the breakthrough.
They picked up where they left off in the second half when Roman Neustadter went close after bringing the ball down onto his chest and volleying towards goal from the edge of the area, however he sliced the shot, making it easy for keeper Ciprian Tatarusanu.
Andrei Prepelita went close for Steaua at the other end when a ball played through the defence released the midfielder, who tried to lift the ball above the advancing Fahrmann, who made a good save.
Jones headed wide after the hour mark from a whipped-in corner before Steaua defender Lukas Szukala volleyed wide at the other end in the 70th minute as both sides were unable to find the cutting edge.
Cristian Tanase then almost gave Steaua the lead when his 25-yard free-kick looked on course for the top corner before it curled too much and flew wide before Piovaccari directed his header straight at the goalkeeper as his last gasp effort failed to break Schalke's defences.