The 24-year-old, who had entered the field 21 minutes into the second half, dived onto 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 managing to pacify the hosts threat for large periods after going ahead through Federico Piovaccari in the 17th minute.
Murat Yakin made just the 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.
And they were made to rue that missed opportunity just six minutes later when Szukala's fine ball up field picked out the unmarked Piovaccari perfectly for the 29-year-old to race through and easily beat keeper Sommer.
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 their opponents but the final ball continued to evade them, 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 see the match end 1-0.
They were 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 they continue their campaign against Chelsea on November 26, while Steaua's hopes of going through are now slim at best.
