Danes Odense were one of three teams who failed in their bid to qualify for the first time, along with Wisla Krakow and Malmo.
Polish side Krakow fell at the final qualifying hurdle for the seventh time, losing 3-1 at APOEL Nicosia who scored the decisive goal in the 87th minute to win 3-2 on aggregate.
Dinamo Zagreb of Croatia progressed 4-3 overall despite losing 2-0 to Malmo in Sweden.
Racing Genk, who are without a coach, beat Maccabi Haifa on penalties to become the fifth team in the hat for Friday's draw in Monaco where they will be joined by Europe's elite.
Another five clubs will go through on Wednesday, the pick of the matches being troubled Arsenal's visit to Udinese.
Bayern, who have played in 13 of the last 14 group stages, were haunted by the prospect of failing to qualify in the season their Allianz Arena will host the final in May.
However, their tie with Zurich was little more than a minor inconvenience and they effectively booked their place when Mario Gomez scored in the seventh minute of the second leg at the Letzigrund.
NOISY FANS
After that most of the fireworks came off the pitch as Bayern's noisy contingent of fans ignored the stadium announcer and let off firecrackers throughout the game while lightning flashed around the ground on a sticky evening.
Swiss Super League runners-up Zurich were lively but rarely threatening while Bayern forward Franck Ribery was given the freedom of the pitch.
Bayern, though, will be concerned they did not take advantage of the many openings created by the France playmaker's trickery.
"It's a shame the goal came so early," said Zurich coach Urs Fischer. "We saw the difference between domestic and international football."
Villarreal, facing a 1-0 first leg deficit against Odense, struggled to break the deadlock until Rossi struck twice in 16 minutes in the second half.
The Italian, linked with Juventus in the close season, got in front of his marker to open the scoring five minutes after half-time and then rifled in a brilliant volley in the 66th minute. Carlos Marchena added the third goal.
Brazilian Ailton netted twice as APOEL produced more heartbreak for Wisla who had a 1-0 lead from the first leg.
Ailton's second goal came in the 87th minute just as the Poles appeared set to end their jinx.
Dinamo, national champions for the last six seasons, took a 4-1 lead to Malmo but were made to suffer after Sime Vrsaljko was sent off in the 50th minute.
Wilton Figueiredo put Malmo ahead from a 69th-minute free-kick. Pontus Jansson then scored to set up a tense finale and the visitors held on thanks to some fine saves from goalkeeper Ivan Kelava.
Genk beat Israelis Maccabi 4-1 on penalties, after winning the second l
