Both of these teams probably hoped at the beginning of the year that they would have bowl berths wrapped up by this time. Or, at least in Tennessee's case, to be on the cusp of bowl eligibility with two likely wins on the horizon. That's not precisely the case.
In the case of Missouri, it's almost impossible to see the Tigers getting to the postseason if they lose this one. They would then need to run the table against Syracuse (likely) and in the trip to College Station at the end of the year. For Tennessee, a loss here would mean the Vols couldn't split the at Vanderbilt-Kentucky run to close out the season -- they would have to win out, though that's admittedly a less daunting prospect than Missouri faces.
And that's because of the very reason that Tennessee will win this game -- the offense. Missouri's defense is middling by SEC standards, and Tennessee has gotten its yards against much better defenses. Oh, and add in the fact that thea game is at Rocky Top, and the Vols get one step closer to the postseason.
Tennessee 31, Missouri 21