The win kept surging OSU (9-1, 5-1) in first place in the Big 12 South with two games to play. The Cowboys have never won the division.
Hunter ran for 116 yards. Justin Blackmon had 145 yards receiving for the Cowboys, including a 67-yard touchdown catch in the second quarter, his 16th of the season, the most in the nation.
The loss is just the latest home defeat for the reeling Longhorns (4-6, 2-5) who have lost six of their last seven games - four straight at home - just one season after playing for the national championship.
Texas must win its last two games to avoid its first losing season since 1997 and qualify for a bowl game.
Oklahoma State - which has more than 50 players from the state of Texas - quickly buried the ghosts of the losing streak and delivered some serious payback for all those years as the latest team to jump on the Longhorns.
Weeden didn't have much personal experience with all that losing. The 27-year-old junior played a few years of minor league baseball in the New York Yankees organization before returning to football, and he carved up the Longhorns with ease when given the chance.
And just like UCLA, Iowa State and Baylor before them this season, Oklahoma State players were singing with their fans in the corner of Royal-Memorial Stadium before dancing out with their big win.
The Cowboys rolled up 308 yards in taking a 26-3 lead into halftime. Jeremy Smith ran for a touchdown and Weeden connected with Blackmon with a perfect throw for the touchdown that beat good coverage by Texas' best cover cornerback, Aaron Williams.
Blackmon, who caught just two touchdown passes in 2009, now has at least one in every game he has played this season. He would have had another against Texas but dropped an easy score in the first quarter.
Hunter scored the final touchdown of the half on a powerful 9-yard run when he started to his left, beat two defenders with a sharp cutback and beat two more at the goal line.
Texas had 1 minute, 15 seconds to try to make something happen, but Garrett Gilbert threw his 15th interception of the season to set up Dan Bailey's second field goal of the half.
Gilbert finished with 202 yards passing and kept his mistakes to a minimum. But he was constantly pressured behind a line with three freshmen starters and was missing key wide receiver Marquise Goodwin, who was at a family funeral.
Texas was held without a first-half touchdown for the fourth straight game.
In the third quarter, Hunter scampered 37 yards to the Texas 1 on a screen pass. He put the game away on the next play with his second touchdown that made it 33-3.
In 2004, 2005 and 2008, Texas rallied from double-digit deficits against the Cowboys. There was no chance of that this year, not in a season that has been nothing short of a shocking collapse by the Longhorns.
Texas didn't cross midfield from late in the first quarter until late in the third against a Cowboys defense that came in giving up an average of 28 points.
Texas hadn't lost four in a row at home in the same season since 1956, the year before Darrell Royal arrived to turn the program into a national power. Mack Brown did the same thing since his first season at Texas in 1998.
Now the Longhorns are in serious danger of a losing season. Texas must beat Florida Atlantic next week and No. 23 Texas A&M on Thanksgiving night just to get to 6-6 and qualify for a bowl. Both games are at home, where Texas is 1-4.
Texas began the season ranked No. 5 and a favorite to win the Big 12. The Cowboys were supposed to finish near the bottom of the league.
That was before Weeden, Blackmon and Hunter started slicing up defenses and the Cowboys started romping through the division. The Cowboys are the only 1-loss team in the South with games at Kansas and home against rival Oklahoma remaining.
The Cowboys also got their first win in Austin since 1944, but the schools did not play regularly until the formation of the Big 12 in 1996.