Debutants Unirea stretched the Rangers keeper with several shots in the first half, including a powerful 30-metre free kick by defender Vasile Maftei.
Rangers looked less dangerous but a powerful long-range strike by midfielder Lee McCulloch hit the wet ground before going past Unirea goalkeeper Giedrius Arlauskis in the 79th minute.
"There were plenty of chances and we had most of them," Unirea coach Dan Petrescu, a former Chelsea fullback, told television station TVR 1.
"We proved once again that we deserve to play in the Champions League but we want to win against Sevilla to be sure we qualify for the next round."
Rangers had looked set to get their revenge after a 4-1 defeat by the Romanians in their previous encounter, until Onofras's long-distance strike.
Onofras said the team from rural Romania, whose stadium holds just 7,000 fans and does not measure up to UEFA requirements, would keep their feet on the ground.
"It's not about luck. Pain and hard work is our recipe and we will use it for the rest of the group matches," Onofras told TVR 1.
There were minor clashes between Rangers fans and stewards, with some seats at the Steaua stadium being ripped up, but Bucharest police said they did not have to intervene.
Sevilla qualified from Group G with a 1-1 home draw with VfB Stuttgart.
