Pertinent tie breakers are:
Division
Common opponent
Conference
Conference we have them now by one game (all their losses are to NFC teams where only three of ours are).
Now that they lost to Detroit, common opponent is getting closer - we both lost to GB. We lost to Tennessee who they beat, they lost to Detroit who we beat. But one of their losses is to Carolina who we don't play - so they currently have us by one game (our loss to SF).
So what it comes down to is this:
We need them to lose to either the Colts or Cowboys - both likely IMO - while we finish one game ahead of them.
The only way we can finish with the same record as them and win the division is if we beat the Seahawks, Vikings and Niners - lose to the Ravens - and they lose to Seattle (in this example, we could lose to the Vikings as long as they lose to the Colts for common opponents to be even).
In that scenario, we would both finish 11-6 or 12-5 and we would win the tiebreaker on conference record because division and common opponents would be tied.
But if they beat the Colts, lost to the Cowboys and Seahawks.
And we lose to the Vikings and Ravens - they would have the tiebreaker over us via record against common opponents.
To summarize:
The way the Cards are playing, they're going to lose both upcoming games so as long as we finish 3-1, division should be ours.