WACO, Texas (AP) - Robert Griffin III turned to his left and threw one of the easiest passes possible, a screen to Terence Ganaway at the line of scrimmage.

Ganaway hardly even reacted and the ball fell to the ground. It was a rare incompletion for Griffin, and hardly his fault.

So what did he do on the next snap? He threw to Ganaway again, and the senior running back turned it into the first touchdown catch of his career - one of five TD passes by Griffin, each to a different receiver, in leading No. 17 Baylor to a 56-31 victory over Rice on Saturday night.

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Incompletions are more noteworthy than touchdowns for Griffin. Look at the numbers through three games: 13 touchdowns, 12 incompletions.

``That's an unreal stat,' Griffin said. ``The guys on the sideline, they're trying to calculate it. They know I haven't been throwing many incompletions. They said, `Now you're one up on it.' ... It's just crazy. They say it's like video games.'

The dazzling junior known as RG3 is pretty unreal, too.

He came into the game leading the nation in passing efficiency and third in total yards, and went 29 of 33 for 338 yards, with another 51 yards and a touchdown rushing. He didn't even play the fourth quarter, leading Baylor to 56 points in just three periods.

The Bears scored 50 points against TCU's vaunted defense in the opener, and 48 points in a game called after three quarters because of bad weather. It's the first time in school history they've cracked 40 in three straight games.

Griffin became the school's career leader in completions, and added another dimension for his Heisman Trophy credentials - a 39-yard punt on a quick kick, the only time Baylor punted all game.

``Robert Griffin is one of the greatest I have ever seen as a player and a coach,' Rice coach David Bailiff said. ``What he is and what he worked himself into this season compared to last season is just frightening with where he can take his game.'

Griffin's night had one flaw: a fumble at the end of a 26-yard run. He was inside the 10 and surrounded by five Rice players. The smart move would've been to slide, but the former hurdler was ready to go airborne when a defender coming from behind popped the ball out. Griffin took a jarring hit and was slow to get up, but halftime quickly followed and he was back to full strength by the third quarter.

``You can go out in a blaze of glory and try to jump, or you can live like a sissy and get on the ground, and I chose the blaze of glory route - and it was a blaze,' Griffin said.

Baylor coach Art Briles probably cringed at the time, more because of the hard hit than the fumble. But he liked the spirit it represented.

``When you're out there, you have to take advantage of every play, and he does,' Briles said. ``If you like green and gold, that should make you smile.'

The Bears (3-0) are assured of remaining in the Top 25 for the fourth straight week, continuing their longest run since 1991. They will be expected to beat Kansas State and Iowa State before the big test: back-to-back games at Texas A&M and Oklahoma State.

Baylor is off to its best start since 2005, and fans are paying attention. A crowd of 40,088 made it three straight of at least 40,000, something that's happened only in 1995 and 1975.

``We're having a lot of fun,' Griffin said.

Rice (1-2) was coming off a win against Purdue, its first against a team from a BCS conference since 2001, plus a bye week. Yet the Owls could never keep up with their former Southwest Conference rival.

Griffin led Baylor to touchdowns on five straight drives and a 35-7 lead. Some breakdowns on defense and special teams helped Rice start to make things interesting, but then a tipped pass was intercepted by Bears defensive back Ahmad Dixon and returned 55 yards for a touchdown.

The next time Baylor had the ball, Griffin threw a 64-yard touchdown pass. He didn't throw at all on the next series, with the Bears going 72 yards in seven plays, all on the ground; Griffin's only carry was the final 4 yards.

``We needed to have flawless execution,' Bailiff said. ``There were too many mistakes to come out of here with a win.'

Rice's Taylor McHargue was 23 of 38 for 260 yards and three touchdowns. He ran 14 times for 44 yards.

Vance McDonald caught six passes for 59 yards and two touchdowns. Andre Gautreaux had the other TD catch, on the first catch of his college career.

Kendall Wright caught 11 passes for 108 yards and his 20th career touchdown, setting the Baylor career record. He's already the career record-holder in catches and yards.

Tevin Reese had seven catches for 106 yards, including the 64-yarder that was his first career touchdown catch.

Ganaway had 78 yards and a touchdown on 17 carries. Glasco Martin ran six times for 76 yards.