That one of these two entries won't make the Final Four speaks volumes about how, uh, blessed Mizzou fans have been...
Kansas 24, Mizzou 7 (1960)
Mizzou was No. 1 for the first time and just needed to defeat Kansas at home to win their first national title. They had taken down Penn State, they had romped over Oklahoma in Norman ... and they completely ran out of gas in the finale. Bert Coan and the Kansas backfield dominated the Tigers, and though they tried to put together a late charge, it was not to be. Kansas prevented Mizzou from winning the national title, and if that was the whole story, it would be enough to make this bracket. Losing your only shot at a title at the hands of your chief rival, on your home field no less? Ouch.
[T]he committee voted 5-3 that KU was in violation of the ban on off-campus recruiting, thus concurring with the mid-season NCAA finding. By a corollary conference rule, this determination automatically rendered Coan ineligible. The next step for the conference committee was to determine the period of ineligibility. Prior to the KU-MU game, speculation in Lawrence was that "If the league fathers rule Coan ineligible, that probably will mean the forfeit of all the conference games he has played in, as well as meaning he won’t be able to play his junior and senior season." However, the conference was more lenient. After two motions to make Coan ineligible for the 1961 season were defeated, the committee voted 6-2 that Mr. Coan would be ineligible to participate in intercollegiate competition in football only for the period October 26, 1960 through October 25, 1961 (a one-year period starting from the date of the NCAA ruling).
KU had gambled that the Big Eight would not back MU on the actions threatened in MU’s November letter, had lost, and they now had to pay the price. KU was ordered to forfeit its victories over CU and MU, and the conference championship was awarded to MU.
It is a very "Mizzou" thing to do to rank No. 1 in the final week of the season, finish "undefeated," and still lose the national title. But that's exactly what Mizzou did in 1960.
Colorado 33, Mizzou 31 (1990)
Asked about the five downs, head referee J.C. Louderback deferred all comments to the Big Eight office, then said, "Our record on the field as officials is that they scored on fourth down."
Asked if there was any provision in the rules to remove a touchdown once scored, he added, "Only if there would be a penalty at that point."
There was none - and No. 12-ranked CU won its third consecutive game (4-1-1 overall) and its Big Eight opener. Afterwards, CU coach Bill McCartney emerged from his locker room and preferred to berate Faurot Field's artificial surface rather than address the five-down fiasco.
"The biggest story is that field is not playable," bellowed McCartney, referring to CU ball carriers or receivers losing their footing at least 15 times. "No one should have to play on that field. You can't even make a cut on that dang field.
"It's a joke to college football to try to run an option attack on that field. We slipped and slid all day, or we would have put more points on the board; I'll tell you that."
Retaliated MU coach Bob Stull: "They get five downs and he's crying? We should have stopped them on fifth down."
Hey Coach, you did.
What made the Fifth Down such an infuriating moment in Mizzou's history wasn't even that the Buffs got an extra down. Or it wasn't just because of that. If Johnson had scored easily on fifth down, and if Bill McCartney had expressed nothing but conciliatory regret after the game, it still would have been a historic occurrence. But Johnson didn't score easily on fifth down -- he almost certainly didn't score at alll -- and McCartney announced that his team basically deserved an extra down because of the shoddy playing surface. (And then Colorado won the national title, in part, because of another iffy-at-best call that enraged Mizzou fans all over again.)
The Fifth Down was the call that set off, basically, two decades of self-pity within the Missouri fanbase. Mizzou fans were already somewhat paranoid and guarded, feeling by nature as if they were basically playing by a different set of rules than everybody else. This game confirmed that, at least for one play, they were.