"I told them, `If you run it, I'll win,"' Edwards said. "So, we called it and I scored."
Edwards' 38-yard touchdown catch sparked a string of 28 straight points, and Houston pulled away to beat Tulsa 48-16 on Friday and earn a spot in next week's Conference USA championship game.
Case Keenum threw for 457 yards and five touchdowns and Edwards finished with 181 yards receiving and four scores as the Cougars (12-0, 8-0) set a school season record by winning their 12th game. The 12 straight wins also match the school's longest winning streak, set over the 1990 and '91 seasons.
"12-0 is pretty good. That's a pretty good position to be in," Keenum said. "I couldn't ask for anything else."
Houston will go for more next Saturday, when they host either Southern Mississippi or Marshall in the C-USA title game. With a win, the Cougars will earn their first BCS bid and become from first team from the conference to play in the Bowl Championship Series.
"Fifteen weeks ago, we set out for one goal and that goal has not changed all year," coach Kevin Sumlin said. "I think a lot of people have tried to talk our team into all these other scenarios and stuff that's happening out there
"Our guys understand that and they've put themselves in a position to achieve that goal. Along the way, there's been a bunch of records broken and a bunch of milestones crossed, but the ultimate goal for us from day one was to win the conference championship."
Keenum helped Houston pull away by hooking up with Edwards twice for touchdowns on fourth down in no man's land. He found Edwards cutting across the field for a 33-yard score on fourth-and-10 in the second quarter, then threw a deep ball to him for a 38-yard TD on fourth-and-1 in the third quarter.
"I think that that's what championship teams do is come through in those big moments -- the championship moments," Keenum said. "We've got a chance to play for another championship at our place, which we couldn't ask for anything more."
Edwards broke the school record by surpassing 100 yards receiving for the 16th time in his career and also broke the Conference USA career record for receiving yardage that was held by Rice's Jarett Dillard.
It figured to be the toughest test yet for Houston, facing C-USA's top defense and a team that also came in without a loss in league play. Tulsa (8-4, 7-1) was allowing only 16 points per game in league play but couldn't keep up once its offense started sputtering in the second half.
"They have to go win a conference championship, but they are well deserving of a BCS bowl," Tulsa coach Bill Blankenship said. "We were playing pretty good coming in here and they shut us down pretty well."
Tulsa got only three points out of two drives with favorable field position in the third quarter. After Curnelius Arnick recovered a fumbled exchange between Keenum and running back Charles Sims, the Golden Hurricane got only 1 yard before settling for Kevin Fitzpatrick's 51-yard field goal to cut the deficit to 20-16.
Tulsa got the ball back again at midfield but again failed to get a first down and punted the ball back to set up an 80-yard scoring drive by the Cougars capped by Edwards' 38-yard score.
Sumlin credited his defense with giving the offense time to "get off the mat."
"We know as a defense that it is a matter of time before the offense can get going. And once they get rolling, it's hard to stop them," said linebacker Marcus McGraw, who had three tackles for loss among his 15 stops.
Michael Hayes added a 1-yard plunge that had to be reviewed before Houston was awarded a touchdown, and Keenum tacked on an 8-yard TD pass to Justin Johnson set up by Edwards' 51-yard reception.
Edwards' final score came on a 14-yard pass from backup Cotton Turner, who replaced Keenum following G.J. Kinne's interception with 6:55 left in the game.
Kinne finished with 176 yards, one touchdown pass and two interceptions -- both as he tried to mount a rally against a defense that hasn't allowed more than seven fourth-quarter points in any game this season.
"It's a hard pill to swallow," Kinne said, "but we lost to a better team today."
Fitzpatrick also matched his career-best with a 52-yard field goal that cleared the uprights easily with a steady wind gusting to around 35 mph, and he connected a 36-yarder.
All four of Tulsa's losses this season have come against teams ranked in the top 10 at the time -- Oklahoma, Oklahoma State, Boise State and Houston.