The home side took the lead on 28 minutes through a header from Florin Gardos, but the visitors equalised just four minutes later thanks to a superb free-kick from Dries Mertens.
However, Steaua took control of the game with two goals inside two minutes early in the second half from Bogdan Stancu to claim their first win in this season's competition.
A lively game produced plenty of chances for both sides and Steaua goalkeeper Cristian Tatarusanu had to be quickly off his line twice in the opening five minutes to snuff out promising Utrecht attacks.
At the other end, Iulian Apostol fired narrowly wide from long distance before Utrecht responded immediately with Edouard Duplan seeing his header tipped over the bar by Tatarusanu.
Midfielder Jan Wuytens then fired wide for the visitors after Steaua failed to clear a corner, but the Romanian side made the breakthrough just before the half-hour mark.
Apostol's corner caused chaos in the area and Gardos' header was carried over the line by goalkeeper Michel Vorm.
Utrecht's players appealed to the referee that the ball had not crossed the line, but television replays showed the officials had got a marginal decision spot on.
The lead lasted just a matter of minutes however, with the influential Mertens curling a 25-yard free-kick into the top corner with Tatarusanu almost motionless.
It remained 1-1 until half-time, but Steaua quickly turned the contest firmly in their favour in the second period.
After 51 minutes, Cristian Tanase's flick inside was collected by Stancu before he fired left-footed into the net from close range.
And the home fans were still celebrating taking the lead when Stancu doubled their advantage, the striker sliding home Banel Nicolita's cross as the Utrecht players appealed in vain for offside.
Steaua should also have had a penalty on 76 minutes when Alje Schut brought down Eric Bicfalvi just inside the area, but referee Stanislav Sukhina waved play on.
Mertens was refusing to throw in the towel and burst into the Steaua box two minutes later, but Tatarusanu was once again quickly off his line to block the midfielder's shot on goal.
Source: DSG
