Klose's goals came on either side of a superb header from Italian World Cup winner Luca Toni at Munich's Allianz Arena, and made sure Jurgen Klinsmann's team will definitely qualify from Group F alongside seven time French champions Lyon.
"We are very, very happy," said ex-Germany coach Klinsmann, who is in his first season with the German giants. “On the one hand, we are happy that we are through with a game left to play. And we are also happy, because the team is just getting better and better with each game,” he said. “We have the feeling for the last six weeks the team is improving steadily and building momentum. To qualify is a good achievement in itself."
French midfielder Franck Ribery was once again the ace in Bayern's pack of stars as he dominated the midfield.
But the night belonged to Klose, who has three goals from the last two games after scoring in last Saturday's 4-1 Bundesliga win.
Dorinel Munteanu-coached Steaua remain anchored to the bottom of the table and were playing for pride, but still have a chance of UEFA Cup berth.
Bayern's Argentina defender Martin Demichelis missed his first group stage match with a calf strain he picked up in Munich's victory against Energie Cottbus last Saturday.
Belgium's Daniel Van Buyten took over, while Lukas Podolski, who has applied for a transfer in January's winter break, was again on the bench and is suffering from a back problem.
Bayern began by battering the Bucharest defence with Toni alone squandering three clear chances in the opening ten minutes as the home side poured forward.
Bucharest had their first chance of the game when Columbian Dayro Galindo went close on 17 minutes, but his shot flew over the bar with Bayern's goalkeeper Michael Rensing beaten.
Having had a first-half goal disallowed, Bayern's Germany striker Miroslav Klose finally got his deserved score when Ribery - sporting pink boots – had his shot charged down.
Klose pounced on the rebound and stabbed the ball home on 57 minutes and then turned goal-provider just four minutes later.
A clever reverse header from the Polish-born forward fell perfectly for Toni to smash home a diving header and suddenly Bayern were 2-0 up with just over an hour played with a foot in the next round.
And the game was ended as a contest with a second goal from Klose when Ribery put him in space and the top scorer from the 2006 World Cup hammered his second home on 71 minutes.
With time running out Steaua's second-half replacement Antonio Semedo from Portugal went close ten minutes from time, but Rensing held his ground and palmed the ball over the bar.
Bayern will now travel to Lyon on December 10 to decide who wins Group F, while Steaua host Fiorentina the same night in Bucharest with a UEFA Cup place at stake.