In the only other match on Sunday Schalke's Klaas-Jan Huntelaar scored twice in their 2-1 win at Hamburg to lift them to fourth on 15 points, four behind Bayern.
While Bayern's players spent the day sunning themselves and drinking beer at their city's Oktoberfest, Bremen were quickly a goal down when Norwegian Abdellaoue converted a third-minute penalty.
The 25-year-old forward added another goal in the 38th minute before Austrian Arnautovic pulled one back on the stroke of halftime when he rifled in a low shot.
Hanover, who also won their Europa League match against Vorskla Poltava in Ukraine in midweek, responded on the hour with Abdellaoue completing his hat-trick and scoring his sixth league goal of the season when he tapped in a cross from close range.
Claudio Pizarro, who had hit the post in the 48th minute, thundered in a volley with seven minutes left to give his 10-man team some hope but they failed to find the equaliser.
Schalke, with new coach Huub Stevens on the bench, took a 13th minute lead with Klaas-Jan Huntelaar wrong-footing the Hamburg keeper Jaroslav Drobny with a header.
The hosts, having scored their first win only last week under interim coach Rodolfo Cardoso, battled back with Croat Mladen Petric firing in from the left for the equaliser.
Spaniard Raul came close for Schalke heading onto the crossbar early in the second half but Huntelaar was on target in the 73rd minute, flicking in a cross from Christian Fuchs.