Texans General Manager Nick Caserio said there was a 99 percent chance they would keep the No. 3 choice, and they did by selecing LSU cornerback Derek Stingley Jr. Caserio, though, gave it only a 50-60 percent chance they would use the 13th overall choice.
The Texans traded the pick to the Eagles, who moved up to select Georgia defensive tackle Jordan Davis.
The Eagles gave up picks No. 15, 124, 162 and 166 to Houston to leapfrog the Ravens.
In four years at Georgia, Davis made 91 tackles, 12.5 tackles for loss and seven sacks. He earned unanimous All-America honors last season and earned the Chuck Bednarik Award and Outland Trophy.
He becomes a future replacement for Fletcher Cox, a first-round choice of the team in 2012.