Ok so the way I read this question is that such a loss has to have a ripple effect on the losing team for a long period.
In that respect, all the Nebraska wins should suffice because the first one marked the beginning of a steep decline for that program from which they've still not recovered. They had a 9-2 season under first year head coach Bob Devaney back in 1962. Between that and the inaugural Big 12 season of 1996 (34 years), they won at least 9 games in all but 2 seasons (went 6-4 in both '67 and '68). They won at least a share of the MNC 4 times in that period. Over their very loud objections about Texas joining the Big 12, they faced that same Texas in 1996. They did manage to win an MNC in 1997 and made an appearance in the 2001 game, but that 1996 Big 12 CCG marked the beginning of the end. After Miami tossed their limp corpse into the Pacific Ocean, they became an average program at best. Yes, that 1996 game certainly qualifies and I would rank that one ahead of the subsequent defeats.
Aggy wins in 1995 and 2011 certainly qualify.
2006 Rose Bowl certainly qualifies, although I'll say the subsequent NCAA sanctions that came down on them also had a lot to do with their slouching into mediocrity.
Here are some lesser known ones, largely because they weren't seen as significant wins by UT fans over an extended period:
2008 vs. Kansas. Kansas just came off a BCS bowl win in the previous year, had a solid team coming back the next year. Texas wins 35-7. That was their final loss of what wound up being an 8-5 season, and they haven't won more than 3 games in any year where Mangino was not the HC. Again, the impact of the win was mitigated by subsequent revelations of Mangino's conduct towards his players, which ultimately led to his ouster.
2009 vs. Texas Tech. Like Kansas the year previous, they were coming off the best season in school history. They lose to Texas by 10, ultimately lose 3 other games, Leach gets railroaded by alumni who were reluctant to increase his salary (in fact, the Chancellor of the University would go so far as to commit perjury in order to give the appearance of legitimacy of his for cause termination). Again, mitigating factors, but a loss to Texas is included and Texas Tech has still yet to win 9 games in a season since 2009.
1989 vs. Oklahoma. Gardere's personal first of four in a row, the team ultimately goes 5 out of 6 through 1994 and 7-2-1 to close out the decade of the 1990's, which was easily the worst decade for Oklahoma football. Of course they've since made it back, but it took quite a while .