On September 21, 1968, the Houston Cougars went to Austin and tied the #4 Texas Longhorns, 20-20. Paul Gipson ran for 173 yards and three touchdowns in the most consequential non-win in UH history.
“It was a great game, just one heck of a game,” Bill Yeoman said in the postgame locker room meeting with the media. “Nobody really likes a tie, but there’s no sense in slashing your wrists and rolling on the ground.”
UH went ahead in the first quarter on a Gipson run before UT tied it up a minute later. Both teams went scoreless in the second quarter. Longhorn Chris Gilbert scored his second rushing TD of the game in the middle of the third. Two plays later, Gipson sprinted 66 yards around the right edge to tie it up again. After a UT punt, Gipson scored his third touchdown, but Terry Leiweke missed the PAT. UT scored in the middle of the fourth to tie it but also missed their PAT. UH marched down the field with a chance to win it late but was stopped inside the one.
When UT got the ball back inside the one, Royal decided to just let the game end in a tie.



The UT players accepted the decision, at least publicly, but weren’t happy with the reaction from their fans.
“When the fans start booing you, it really hurts. It’s kind of disappointing, but I guess you have to get used to it,” halfback Ted Koy said. “UT players, for the last 50 years, have gotten used to it.” Texas sat on the ball and accepted the tie.
“We played a great team with some outstanding athletes. Any team that can stop our offense on the one-foot line is playing tremendous defensive football,” Yeoman said. For his part, UT coach Darrell Royal went into the UH locker room and told the team how much he appreciated what they did.
“I just want to tell you we’ve got all the admiration in the world for you,” Royal told the UH players and staff. “Offensively, we haven’t played a better team.
“I’ve only been in (the visitor’s) dressing room twice. That shows what admiration I’ve got for you.”
When Royal finished speaking, the UH players cheered his words.
“They have a fine football team,” UT player Corby Robertson said. “I wouldn’t mind a rematch in the postseason.” Robertson is the grandson of Hugh Roy Cullen and the son of Corbin Robertson, both UH giants.
When told a rematch was impossible because UH was on probation, Robertson spat out “damn it!”

The play of Paul Gipson blew away Texas. All-SWC defensive tackle Loyd Wainscott said Gipson was “the best runner I’ve ever faced. I’d put him above (OJ) Simpson of Southern Cal because he doesn’t get knocked down. You can stick him right in the mouth, and he’ll still get away.”
“I know once we hit (Gipson) over by our bench just as squarely on the nose as we could,” Royal remarked after the game. “He just bounced off and nearly scored.”
The game proved to many that Houston belonged on the big stage. Darrell Royal believed it, and that night in 1968 marked one of the first steps that helped UH gain entry into the SWC.