Bush, an off-season free agent signing, racked up 90 rushing yards on 21 carries and added 101 yards with a score as a receiver.
Matthew Stafford (28-for-43, 357 yards) tossed both of his touchdown passes in the second half for for the Lions (1-0), who finished last season with an eight-game losing streak.
Minnesota's Christian Ponder managed to complete just 18-for-28 passes for 236 yards with a touchdown, three interceptions and a lost fumble.
Reigning NFL MVP Adrian Peterson ran for a 78-yard touchdown on his first carry but gained just 15 yards on 17 attempts the rest of the way for the Vikings (0-1).
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