Texas, which dropped to 0-6 in Big 12 championship games, whittled a 48-33 halftime deficit to 66-52 with about 8 minutes left, taking advantage while Marcus and Markieff Morris sat on the bench with three fouls.
But after Taylor and J'Covan Brown swapped 3-pointers, Tyrel Reed hit an uncontested 3 and rebounded a Texas miss, leading to Markieff Morris' tip-in for a 68-55 lead. A moment later, Reed's steal led to Markieff Morris' free throw.
Jordan Hamilton had 21 points for second-seeded Texas (27-7), which beat Kansas 74-63 and snapped the Jayhawks' team-record 69-game home court winning streak on a melancholy afternoon in January.
The night before, the mother of sophomore forward Thomas Robinson had died unexpectedly. Players and coaches were up most of night trying to comfort the grieving young man, who had also lost both grandparents a few weeks earlier and was now left virtually alone with his 7-year-old sister back in Washington, D.C.
While Kansas never tried to use Lisa Robinson's death as an excuse for its first home loss in almost four years, a pall hung over Allen Fieldhouse that afternoon and the players did seem physically and emotionally spent.
Marcus Morris, who stood next to Robinson during the national anthem that day and wept, had 17 points Saturday as the top-seeded Jayhawks (32-2) beat the Longhorns in the Big 12 title game for the fourth time in four tries and wrapped up a nearly certain No. 1 seed in the NCAA tournament.
Taylor had a season-high 20 points and five assists. Robinson had 10 points and nine rebounds and got some of the biggest cheers of the night from the hugely partisan Kansas crowd in downtown Kansas City's Sprint Center.
The Morris twins were a collective 5 for 6 in the opening minutes before Taylor's steal keyed a 10-2 run that left the Jayhawks with a 27-15 and triggered a roar from the crowd.
Brown's 3-pointer trimmed the lead to 71-63 with about 5 minutes left, but the Jayhawks answered with Brady Morningstar's breakaway bank shot, Robinson's tip-in and two buckets by Marcus Morris.
Markieff Morris had 14 points and nine rebounds, Morningstar had 13 points and Reed had 11 as the Jayhawks, the regular-season Big 12 champions the past seven years in a row, won their eighth conference tournament title in 15 seasons.
Brown had 17 points and Cory Joseph 14 for Texas, which shot only 41 percent while the Jayhawks hit 57 percent.