Nineteen minutes remained when Steve Staunton's 50-yard ball caught Steaua's defenders off guard. With his seldom-used right foot, Milosevic buried a low shot. Villa confirmed their superiority over fellow former European champions four minutes from time, Ian Taylor racing on to Lee Hendrie's pass before firing home.
Villa achieved the victory which keeps their season alive at least until March without their leading scorer, Dwight Yorke, who had failed a fitness test on a calf injury. In the event, the Tobagan had done his bit with the away goal in a 2-1 defeat in Bucharest, and he was not missed as badly as Brian Little may have feared.
Glenn Hoddle was not present, despite the opportunity to run the rule over three or four of England's opponents next summer. Not that Little was complaining. "We've saved our best form for this competition," the Villa manager said, "and we've needed to."
Taylor, filling Yorke's role of attacking from midfield, took over five minutes to test Zoltan Ritli in Steaua's goal. The goalkeeper did well to touch over his volley as it raged towards the spot beneath the angle of post and bar, but was beaten when Staunton unleashed a free-kick towards the same point. To Villa's frustration, the ball struck the bar and flew over.
Stan Collymore's goal against Coventry on Saturday, only his second in 18 appearances since his pounds 7m transfer from Liverpool, had clearly done wonders for his confidence. A bold, twisting run carried him past three defenders and into the penalty area. Ritli beat aside the ensuing drive with considerable difficulty.
Whatever the truth of the rumours that Collymore is short of allies in the Villa dressing-room, he certainly linked effectively with Mark Draper. The first-time volley with which he lifted the midfielder's cross narrowly over the bar was the sign of a striker trusting in his instincts. Collymore soon returned the compliment with a selfless centre, but heading is not Draper's strongest suit and the ball looped harmlessly over.
Steaua, who have been rebuilding with youthful talent after selling most of their senior players abroad, were content to soak up the pressure and strike on the break. Their strategy almost reaped a rich reward in the 49th minute when the two pinpoint passers, Marius Lacatus and Cristian Ciocoiu, worked the ball from the centre circle into the Villa box via the left wing. Damian Militaru arrived and took aim, only for Mark Bosnich to parry leaping to the left.
The effect of Steaua's near miss was to raise the decibel level among the crowd. Like their team, they had adhered to Little's plea for patience. Now they felt it was time to go for broke.
From a Staunton free-kick whipped in from the right, Taylor's glancing header brought a diving save from Ritli. Continuing his passable impersonation of Yorke, Taylor then surged through to shoot off Milosevic's pass. Reaching the ball a split second before the goalkeeper plunged at his feet, he lifted his shot into the Holte End.
With nearly a third of the match remaining, Little sent on the 20-year- old Hendrie. It was another sign that the time for caution was past. When Collymore blazed wide and then saw his point-blank effort scrambled off the line by Tibeiru Csik, Villa may have feared it was not to be their night. Milosevic and Taylor dispelled their doubts to cacophonous approval.
Aston Villa (1-2-5-2): Bosnich; Staunton; Ehiogu, Southgate; Charles, Taylor, Grayson (Hendrie, 62), Draper (Nelson, 82), Wright; Collymore, Milosevic. Substitutes not used: Joachim, Curcic, Scimeca, Collins, Oakes (gk).
Steaua Bucharest (1-2-5-2): Ritli; Rachita; Csik, Matei; Reghecampf, Rotariu, Militaru (Lincar, 88), Munteanu, Miu; Lacatus (Luca, 68), Ciocoiu (Hrib, 77). Substitutes not used: Baciu, Raducan, Mozacu, Gherasim (gk).
Referee: B Heynemann (Ger).