At present, some websites are reporting that the Packers own the tie-breaker against the Vikings because they have a better record against common opponents, which is the third criterion for breaking division ties between two teams (after head-to-head records and won-lost percentage against division opponents).
What those breakdowns fail to take into consideration however is that record against common opponents will be moot by the end of the season, because the Packers and Vikings have already played their two games against uncommon opponents this season and went 1-1: the Packers defeating the Tampa Bay Buccaneers and losing to the Philadelphia Eagles, while the Vikings defeated the Atlanta Falcons and lost to the New York Giants.
In other words, the Packers may hold the edge over the Vikings against common opponents at present, but Minnesota has yet to play the Kansas City Chiefs and Arizona Cardinals, two teams the Packers went 0-2 against, while the Packers have yet to play the Oakland Raiders and Denver Broncos, teams the Vikings went 1-1 against.
Thus, by the end of the season -- when it matters -- if the Vikings and Packers are tied overall, their records against common opponents will be identical.
The next tie-breaking criterion is record against conference opponents. In order for the Vikings (7-4) and Packers (7-5) to tie on that mark, the Vikings must lose to the Cardinals in the final week of the regular season.
