Both the Washington Huskies and the Washington State Cougars are relatively good at controlling the ball.
However, perhaps the biggest reason WSU went into halftime up 45-43 is forcing UW into 10 turnovers in addition to shooting 50 percent from the field. Even if you attribute that to early big game jitters, you also have to take into consideration that the Huskies really struggled to find a rhythm against the WSU zone early.
As might have been expected, Klay Thompson is a big reason for WSU entering halftime with a lead, finishing the half with 11 points on 5-for-10 shooting despite actually being contained relatively well by the Huskies' defensive combination of Justin Holiday and Terrence Ross.
However, the more important player going forward might be DeAngelo Casto and his ability to continue rebounding as he entered halftime tied for a game-high 11 points and a game-high seven rebound. But Casto will still need help with three fouls- despite his effort, UW beat WSU 9 to 3 on the offensive boards which is a primary reason WSU isn't further ahead.
That said, over at the UW Dawg Pound game thread, someone noted that at some point in the first half FSN commentator Ernie Kent said, "That’s what makes Washington so good. They have 8 scorers in the game right now.” And despite the fact that it's a 5-on-5 game, UW seemed to find shooters everywhere - at one point during the first half, they were shooting 5-for-10 from beyond the arc. They got scoring from a number of people with Darnell Gant having a team-high nine points and Terrence Ross with eight points and shooting 2-for-4 from the 3-point line.