Federico Piovaccari gave the Romanians the lead, which they looked set to keep hold of, but a late goal allowed the hosts to grab a draw.
Giovanni Sio, who had entered the field 21 minutes into the second half, dove on to a ball from Valentin Stocker in the dying stages to tap past Steaua goalkeeper Ciprian Tatarusanu and rob the Romanians of three points.
Sio's goal came somewhat against the run of play with Steaua pacifying the hosts' threat for large periods after going ahead through Federico Piovaccari in the 17th minute.
The Italian notched his first goal in Group E after getting on the end of a fine ball from Lukasz Szukala to go one-on-one with Basel keeper Yann Sommer and fire home.
Murat Yakin made just two changes from his Basel side's 1-1 league draw at Aarau last weekend, with Fabian Schar favoured over fellow youngster Arlind Ajeti while Stocker replaced Mohamed El Nenny.
Steaua coach Laurentiu Reghecampf, in contrast, opted to switch things up drastically from its previous Liga 1 match with forward pair Adrian Popa and Piovaccari two of the six additions.
The home side enjoyed the better chances of the opening spell, and Matias Delgado had a fine chance to put them ahead after 11 minutes with a free kick from just outside the box, but he curled it over the crossbar.
And Basel was made to rue that missed opportunity just six minutes later when Szukala's fine ball upfield picked out the unmarked Piovaccari perfectly for the 29-year-old to race through and easily beat goalkeeper Sommer.
Basel tried to respond immediately and only a good save from Tatarusanu denied it an equaliser after 25 minutes as Mohamed Salah raced down the wing before seeing his square pass cut out.
The half then came to an end with a golden chance for Steaua as Sommer parried a close-range effort directly toward Florin Gardos, but the 25-year-old defender lofted his shot over the crossbar.
The break appeared to serve the hosts well though, and they came very close to pulling the game back level in the 61st minute as Fabian Frei's powerful shot from range was tipped over by the keeper.
Basel then maintained the pressure on its opponents but the final ball continued to evade it, with newcomer Sio smashing straight into Tatarusanu, shortly before Stocker's cross into the box was also blocked.
The visitors threatened to double their advantage in the final minutes too, but there was relief as Cristian Tanase fired his shot directly into Sommer to keep the match at 1-0.
Basel was eventually rewarded for the pressure in the dying stages of injury time though as Sio got on to the end of a fine ball from Stocker to fire home and ensure his team earned a point from the encounter.
Basel will now need to hope to go one better when it continues it campaign against Chelsea on November 26, while Steaua's hopes of going through are now slim at best.