When the Washington Redskins’ team plane touched down in Dallas on Wednesday, the day before the team would face the Cowboys for Robert Griffin III’s first game as a pro in his home state, the rookie quarterback sent out a tweet.

“Back in Texas and on a mission,” Griffin’s message said.

The following day, with family and friends and his former college coach in attendance, Griffin carried out his mission, leading the Redskins to a 38-31 victory over the Cowboys on Thanksgiving Day.

Griffin, who starred in football and track at Copperas Cove High School and won the Heisman Trophy at Baylor University, looked right at home in Cowboys Stadium. He completed 20 of 28 passes for 311 yards, four touchdowns and an interception, and became the first Redskins quarterback to throw for four touchdowns in back-to-back weeks.

“It was good, emotionally, to come back. I got to see my Baylor head coach, Coach Art Briles. Hadn’t seen him in a long time,” Griffin said. “Being back in Texas, I felt like I was back home, where I’ve spent so many years. But it didn’t charge me through the roof. It was a normal game, even though it was a Thanksgiving game. That’s how we approached it.”

Said Redskins Coach Mike Shanahan: “He’s kind of like Cool Hand Luke. He just handles himself and goes about his business, works extremely hard to prepare for a game. . . . He focuses on his job and doesn’t seem to let anything bother him. That’s why he has the success he has, because he’s very disciplined, very determined.”

Griffin’s heroics — along with a 24-carry, 113-yard performance by running back Alfred Morris, a defensive effort that forced three turnovers, and a win-sealing 48-yard field goal from Kai Forbath — gave Washington its first Thanksgiving victory over Dallas in seven tries.

The win was Washington’s second straight — its first two-game win streak since Weeks 1 and 2 of the 2011 campaign — and its second consecutive victory in the NFC East following Sunday’s 31-6 triumph over Philadelphia.

At 5-6, the Redskins are tied for second place in the division. If the New York Giants lose to Green Bay on Sunday night, Washington will host the Giants on Dec. 3 with a share of first place in the NFC East on the line.

Thursday’s nationally televised game had no shortage of fireworks. After a slow start, the Redskins went on a 28-point scoring tear in the second quarter, then had to weather a 28-point second half by the Cowboys and quarterback Tony Romo, who completed 37 of 62 passes for 441 yards and three touchdowns. It also took a strong defensive stand for the Redskins to escape victorious.

“I was really proud of our football team,” Shanahan said. “They played extremely hard. It was a little exciting in the second half. We had to make some plays there on that last drive, played eight minutes, had to get a couple first downs. Really impressed with [Forbath] to come up with the big field goal there in the last couple minutes of the game. . . . But more importantly, it was a game we needed, and really pleased with our total effort.”

The Redskins stumbled out of the gate but began clicking on their third possession, beginning the most prolific quarter they have orchestrated in 13 years.

A 68-yard bomb from Griffin to Dallas native Aldrick Robinson ignited Washington, and was followed by an Alfred Morris touchdown run, a 59-yard touchdown strike to Pierre Garcon, and a late-second-quarter six-yard toss to Santana Moss.

Garcon made an impressive catch on his touchdown play. He had to change direction in midair to catch the ball, which was thrown behind him, then stumbled on the way down before regaining speed to reach the end zone untouched.

“I jumped up, closed my eyes and prayed for it. Caught it and stumbled a little, and just tried to give it everything I got and just did what I could,” said Garcon, who had five catches for 93 yards.

With time running out in the half, Redskins cornerback DeAngelo Hall picked off a Tony Romo pass intended for Cole Beasley and returned it 27 yards to the Dallas 33-yard line with 44 seconds left.

Griffin and the offense needed just four plays to find the end zone. On first-and-goal from the 6, Griffin rolled to his right and placed the ball in a tight spot on the back shoulder of wide receiver Moss, who toed the line and maintained possession.

The 28-point quarter marked the first by the Redskins since an Oct. 3, 1999, game against Carolina and put Washington up 28-3 at halftime. Washington outgained Dallas 226-63 in the second quarter.

The Redskins’ offense went cold after halftime, however, and the Cowboys outscored them 28-10 in the final two quarters to make a game of it.

Dallas managed a field goal on its opening possession of the half, and with 3 minutes 5 seconds left in the quarter, Redskins linebacker London Fletcher intercepted Cowboys quarterback Tony Romo, the 20th interception of Fletcher’s 15-year career. But the offense had to punt a fourth time in the third quarter, and the Cowboys capitalized with an 85-yard touchdown pass from Romo to wideout Dez Bryant to cut the lead to 28-13 with 1:38 left in the period.

The Redskins’ offense finally got back on track. Washington went 53 yards in six plays and faced third and inches from the Dallas 29-yard line. With the Cowboys’ defenders playing close to the line, preparing to defend a quarterback sneak, right end Niles Paul ran downfield untouched. He made a leaping catch of a pass from Griffin and fell to the ground at the 4-yard line, got up and stepped into the end zone as the Redskins opened a 35-13 lead with 12:48 remaining in the fourth quarter.

But the Cowboys came right back with an 88-yard drive that culminated in a 10-yard touchdown pass to running back Felix Jones, and Romo scored a two-point conversion on a draw play.

Dallas found the end zone again less than two minutes later. Griffin threw an interception to safety Charlie Peprah, who returned the ball to the Washington 18-yard line. On third and three from the 11, Romo found Bryant in the end zone, and the extra-point attempt pulled the Cowboys within 35-28 with 8:24 to play.

With the Redskins needing a score to protect their chances, Griffin marched them down to the Dallas 30-yard line but could get no closer. Forbath drilled a 48-yard field goal to put the Redskins up 38-28 with 3:03 left.

“That was probably the drive that saved our season,” Griffin said.

Said special teams captain Lorenzo Alexander: “Big time. If you miss that kick, then they drive and have the ball at the 40-yard line and they had good momentum at that point. It’s a whole different game at that point.”

The defense held Dallas to a field goal with 18 seconds left, and Hall recovered an onside kick and returned it to the Cowboys 2 before sliding to avoid giving the ball back to the Cowboys.

Griffin took the field a final time and knelt to run out the final 12 seconds.