The margin of victory could have been greater but for the performance of Steaua goalkeeper Ciprian Tatarusanu, although the visitors may well rue their inability to attack until they were two goals down.
Overturning such a deficit against Frank de Boer's team in Romania is daunting enough, but they must do so without Mihai Pintilii, who was sent off at the death for his second bookable offence.
There was little by way of clear-cut openings in a start which saw Ajax enjoy greater possession without threatening.
The crowd had to wait until the 21st minute for the first real shot on goal, Kolbeinn Sigthorsson's effort from the left of the penalty area parried by Steaua goalkeeper Tatarusanu.
Alexandru Chipciu fired over for the visitors moments later as the game warmed up, with the hosts claiming the first goal in the 28th minute.
Christian Eriksen's cross from the right found Alderweireld in the six-yard box and the defender headed the ball into the bottom left-hand corner of the goal.
Sigthorsson was thwarted by Tatarusanu and the hosts almost doubled their lead shortly before the break when Siem De Jong's right-footed shot was tipped round the post by the keeper.
However, Ajax did not have to wait too much longer before they went further ahead in the 49th minute.
De Jong's ball from the centre of the area found Van Rhijn and his cross-shot found the bottom left-hand corner of the goal.
Steaua needed to find something if they were to return to Arena Nationala with a real chance of cutting the deficit and progressing into the last 16.
Adrian Popa sent in a long-range curling shot which drew a fine parry from Kenneth Vermeer and the Ajax goalkeeper was then equal to Raul Rusescu, blocking his shot from the centre of the area.
Leandro Tatu fired over and Florin Gardos shot wide as the visitors pressed for an away goal, but they were reduced to 10 men in the final minute when Pintilii was sent off, his yellow card for a foul on De Jong his second of the match.
Ajax then came close to all but confirming progression but Tatarusanu kept his side in the tie by repelling Derk Boerrigter.