Hamburg arrived in Belgium holding a fragile 2-1 advantage, but unlike their frenetic second leg at RSC Anderlecht in the previous round, Petrić ensured they would enjoy this return.
The Croatian international opened the scoring in the 20th minute and then struck spectacularly barely 120 seconds after Igor De Camargo's 33rd-minute equaliser.
José Paolo Guerrero put a late seal on a 5-2 aggregate win which sets up a last-four tie with Fulham FC.
Standard's spirited first-leg showing had given their supporters cause for optimism, and Frank Rost had to spectacularly palm away Mehdi Carcela-González's early powerful drive as the hosts sought to fuel that belief. Hamburg, though, possess a bona fide match-winner in Petrić, and he gave the Bundesliga outfit breathing space when he nodded in from close range after Zé Roberto's cross was deflected invitingly into his path.
The Brazilian played an unwitting role in throwing Standard a lifeline, conceding the free-kick from which De Camargo headed the equaliser, but barely had play restarted than the hosts were cut adrift again by the irrepressible Petrić. Dennis Aogo's whipped cross was met perfectly by the airborne forward, who fired into the bottom corner to gasps of amazement from around the ground.
The task of scoring at least three times after the break looked beyond a Standard side lacking their impressive first-leg fluency, though Dieudonné Mbokani almost reduced the deficit with a point-blank shot that Rost instinctively turned away.
With the hosts' sting drawn, Hamburg were able to play within themselves, and Guerrero provided the finishing touch to a sweeping counterattack in added time, ensuring that when the UEFA Europa League trophy arrives in Hamburg next week, the host city's premier club still have a chance of getting their hands on it.
