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Three clinical finishes from Olic -- one right-foot shot, a left-foot shot and a header -- helped the four-times European champions complete a 4-0 aggregate semifinal success to silence the vocal faithful at Stade Gerland.
Olic netted his first after 26 minutes with a neat turn and shot, smashed in a pass from Hamit Altintop after 67 minutes and completed his hat-trick with a header 12 minutes from time.
It was only the second hat-trick in a Champions League semifinal after Alessandro Del Piero's treble for Juventus against Monaco in 1998.
"I didn't think we'd win in such a one-sided manner and that I'd get three goals," Olic told German TV. "That's just incredible in a match like this."
Bayern will face either Inter Milan or Barcelona in the May 22 final at the Bernabeu in Madrid.
"We had a great game, we were well positioned on the pitch and if we play like this all the way, it will be hard to beat us", Bayern's Dutch coach Louis van Gaal told a news conference.
"The players now know what it's like to spend 10 months with Van Gaal, they know it's not easy but they're happy now and so am I."
Lyon finished the game with 10 men after centre back Cris was sent off just before the hour. He was booked for a foul on Olic, then shown a second yellow card for mocking referee Massimo Busacca's decision.
"They were the stronger team. Too bad we failed to equalise (after the first goal) because we had a few chances," Lyon coach Claude Puel told French TV channel TF1.
It was a night to celebrate for Bayern, who had not been in the Champions League final since beating Valencia on penalties nine years ago.
They got off to a strong start, Thomas Mueller missing a clear cut opportunity after two minutes when his low shot from inside the box went a fraction wide.
It was only a matter of time for Bayern, who looked sharper even without the suspended Franck Ribery.
Following a fine one-two with Arjen Robben, Mueller raced into the box, cut it back for Olic, who turned and slotted past the helpless Hugo Lloris in the 26th minute to silence the home fans who had created a deafening chorus before the match.
Lyon missed their chance to level on the half hour when Michel Bastos fluffed a left-footed attempt after Lisandro Lopez had found the Brazilian unmarked at the far post.
Puel replaced Aly Cissokho with striker Bafetimbi Gomis, with Bastos taking the left back position as Lyon tried to step up a gear after the interval.
Bayern still had the upper hand though, a Bastian Schweinsteiger 25-metre volley whizzing over the bar on 53 minutes.
The contest was effectively over just before the hour when centre back Cris was sent off, picking a second yellow card for dissent seconds after being shown the first for a mistimed tackle on Olic.
It did not take Bayern long to make the most of it, as Olic collected a through ball from Altintop before coolly slotting past the advancing Lloris.
He rubbed salt in the wound by adding a third with a powerful header that went under the bar 12 minutes from time.
The Bayern fans chanted Ribery's name, whom they hoped will play the final.
Ribery though will miss the Champions League final after he was handed a three-match suspension by UEFA on Wednesday. The German side have three days to appeal against the decision