Haaland took full advantage of his first start for Dortmund - following two impressive substitute appearances - scoring in the 18th and 76th minutes.
The Bavarian powerhouse said the 24-year-old Odriozola signed a deal to the end of the season after successfully passing a medical examination.
Goals from Thomas Müller, Robert Lewandowski, Thiago Alcântara and Ivan Perisic in the final half hour ensured Bayern made a winning start to the second half of the season and kept the pressure on early leader Leipzig.
Bayern captain Manuel Neuer, the Germany goalkeeper and Bayern’s No. 1 since he joined from Schalke in 2011, has no intention of giving up his place for the 23-year-old Nübel.
As Alexander Nuebel's contract with FC Schalke 04 is running out next summer, he signed a five-year contract with the ruling German champion until 2025.
Substitute Zirkzee scored in the 86th minute for Bayern to beat Wolfsburg 2-0. Serge Gnabry added another in the 89th while the visitors were still recovering.
Bayern Munich said Friday the Polish forward will have the operation shortly after the team's league game against Wolfsburg on Saturday.
In other matches: CParis Saint-Germain coach Thomas Tuchel was paired with his former club, Borussia Dortmund; Lyon will take on Juventus; Tottenham will play Leipzig; and Atalanta will meet Valencia.
Philippe Coutinho starred for Bayern Munich as the side ended its two-game losing run in the league with an impressive 6-1 win over Werder Bremen.
Robert Lewandowski scored two and substitute Thomas Müller grabbed the other as Bayern bounced back from successive 2-1 defeats to Borussia Mönchengladbach and Bayer Leverkusen.
The Bavarian club ended a run of two league losses with a 3-1 win over Tottenham in the Champions League on Wednesday, but has few options ahead of three Bundesliga games in a week.
Kingsley Coman, Thomas Muller and Philippe Coutinho scored for Bayern Munich while Ryan Sessegnon scored for Tottenham Hotspur.
Left-back Ramy Bensebaini scored both goals for Gladbach, which last won the title in 1977. Bensebaini headed in a corner to draw Gladbach level after Ivan Perisic's volley for Bayern, and then scored the decisive penalty in added time.
Borussia Mönchengladbach is trying to turn back the clock to the 1970s. That was the decade when Gladbach was an unstoppable force in what was then West German soccer, winning five league titles, including three in a row.
Lewandowski had extended a contract at Bayern until June 2023 before the 2019/2020 season
Bayer Leverkusen edged past Bayern Munich in a thrilling 2-1 win on Saturday, while a 10-man Dortmund side held on to their lead against Hertha Berlin.
Robert Lewandowski scored four goals in 15 minutes as Bayern Munich cruised to a 6-0 win to win the group in the Champions League.
Bayern Munich routed Fortuna Dusseldorf 4-0 away, while Gladbach lost at promoted Union Berlin 2-0.
Bayern Munich stayed perfect under interim coach Hansi Flick with three wins in three games as it beat Fortuna Düsseldorf 4-0
Robert Lewandowski stretched his Bundesliga record by scoring in each of the opening 11 games this season as Dortmund suffered another heavy defeat to Bayern.
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