The Broncos used a field goal late in the fourth quarter to take the lead, then got an interception on Washington's next drive to seal the game.
Boise State heads into next year looking to bust up the BCS one final time before there's a four-team playoff.
Here's a look at the postgame grades for the Broncos.
Final Game Grade: B+
Joe Southwick had one of his best games of the season as he completed 26 of his 38 passes for 264 yards and two touchdowns.
Southwick did have two fumbles, however, one of which turned the ball over and started Washington on a scoring drive.
His biggest quarter came in the second when he had 106 passing yards, as Boise State scored nine points in the quarter
The junior showed a lot in this game and throughout the year, giving head coach Chris Petersen the confidence next year to open the playbook even more.
Final Game Grade: D+
The running game was almost non-existent for the Broncos.
D.J. Harper was the leading rusher with 72 yards as the Broncos struggled throughout to get anything going. Harper did catch three passes for 14 yards as well, but for the most part, the running backs were a non-factor.
For Boise State, it was surprising, especially considering it came into the game averaging 173.1 yards per game on the ground.
Overall Game Grade: A+
The Broncos got 259 receiving yards from their corps of receivers as Southwick was able to find them time-after-time.
Matt Miller led the team with six catches for 90 yards, while Geraldo Boldewijn had five catches for 59 yards and a touchdown.
Chris Potter had nine catches for 55 yards, while Aaron Burks had one catch for 40 yards.
The Boise State coaches could have asked for more from the receiving group. They did what they were asked to do and didn't make any mistakes.
Overall Game Grade: A+
Holden Huff only had two catches in the game, but both went for touchdowns.
His first was from 34-yards out, while the second was from the 1-yard line.
Huff was efficient with both of his catches and is someone who the Broncos will involve more in his sophomore year next season.
For him to have that kind of an impact as freshman says a lot about the talent he has.
Overall Game Grade: C
The pass protection was good for the Boise State offensive line, but when it came to run blocking, it wasn't good.
The offensive line got very little push on run plays, as the Broncos gained a total of 109 yards on the ground.
In fact, of Boise's 36 rushing attempts, 20 went for two yards or less. That's not a recipe for success.
The offensive line also allowed one sack, which isn't bad considering the amount of pressure Washington had throughout the game.
Overall Game Grade: D+
The defensive line had struggles as well, allowing Washington running back Bishop Sankey 205 yards on the ground.
Sankey had 10 rushes that went for seven yards or more as he continually sliced through the line.
When Washington was throwing the ball, the linemen were able to get pressure on the quarterback as Tyler Horn and Ricky Tjong-A-Tjoe each came up with sacks.
Overall, it wasn't a good day to be a lineman (either side) for the Broncos.
Overall Game Grade: C+
While not spectacular, the linebackers made plays when they had to.
J.C. Percy led the team with 17 total tackles, as he constantly found himself making the tackle.
Tommy Smith was fourth on the team with six tackles.
Overall, the linebackers did a decent job after the defensive line continually let Sankey through the line.
Overall Game Grade: B-
Jeremy Ioane came up with the biggest play of the game as he intercepted a pass with less than a minute to go to seal the Broncos' victory. Had Ioane not jumped the route, Washington likely would have made a reception and put itself in position to kick a game-winning field goal.
Darian Thompson finished second on the team with nine tackles, while Corey Bell had eight.
While Boise State came into the game ranked in the top 10 in the country in passing yards allowed per game, the 242 passing yards allowed wasn't exactly what they were looking for.
Petersen expects more out of his group.
With that said, when it came time for a big play to be made, it was the secondary that stepped up to do so.
Final Game Grade: B-
The special-teams unit was good for most of the game, although the Broncos do need a kicker who can kick longer than 30 yards.
Michael Frisna was 3-for-3 on field goals, while two Boise State punters averaged 36.4 yards on five punts.
On kick returns, Shane Williams-Rhodes averaged 27 yards per return, with a long of 47.
Overall, it was good.
Overall Game Grade: A-
When it came down to it, Boise State head coach Chris Petersen made the right call when needed.
Although the kicking game was shaky, Petersen showed confidence in his kicker as the Broncos got a 27-yard field goal for the game-winning points.
The offense was in hurry-up mode early on before settling into a rhythm and flow in the second quarter.
Petersen and his coaches had his team ready, although most didn't think the game would be as close as it was.