LANDOVER, Md. — After Robert Griffin III was hurt yet again, Kirk Cousins couldn’t miss.

The Washington Redskins lost both Griffin to a dislocated ankle and DeSean Jackson to a sprained shoulder in the first quarter Sunday with injuries that by no means appeared minor. While that might have major repercussions for the season, Cousins and his teammates were able to shrug it off against the woeful Jacksonville Jaguars in a 41-10 win.

Cousins, looking more comfortable in new coach Jay Gruden’s offense than Griffin ever did, completed his first 12 passes and finished 22 of 33 for 250 yards and a pair of touchdowns. Ryan Kerrigan had four sacks and the defense had 10 — both tying franchise records — and Washington didn’t allow the Jaguars past midfield until the final two minutes of the first half.

Washington (1-1) dominated 449-148 in total yards against a Jacksonville team that, combined with the previous week, allowed 55 unanswered points until Chad Henne hit Marcedes Lewis for a 63-yard score with 1:40 to go in the half. The Jaguars are 0-2 for the third consecutive season.

The Redskins ended a nine-game regular-season losing streak — the second-longest in franchise history — and gave Gruden his first win as an NFL head coach, but the future is cloudy because of the health of their two most dynamic playmakers. Griffin dislocated his left ankle and was carted off with his leg in a splint, while Jackson sprained his left shoulder and was supporting his arm and shoulder gingerly as he walked toward the tunnel.

Not surprisingly, the team soon announced that neither would return. Griffin was scheduled for X-rays and an MRI to determine more about his injury. He and Gruden did not offer a timetable for the quarterback’s return, but the injury typically sidelines NFL players for at least two months. If there is also a fracture, Griffin will need surgery and will almost certainly be done for the year.

The prognosis is better for Redskins receiver Jackson, who sprained his AC joint and held out hope that he will be able to play next week against the Philadelphia Eagles.

Griffin has been trying to learn to be more of a pocket-passer under Gruden, but he was hurt while being his typical RG3 self. He made a leaping, across-the-body throw near the sideline while being pursued by linebacker Paul Posluszny, then landed awkwardly on his ankle as he tumbled out of bounds. The pass was caught by Jackson for an 11-yard gain.

After his leg was placed in a splint, Griffin wiped his brow and waved, saluted and gave a thumbs-up signal to the crowd as he was carted along the sideline toward the players’ tunnel. The fans chanted “R-G-3!”

It was the latest setback for a promising but injury-marred career. Griffin missed all or part of four games in his record-setting rookie season of 2012 due to various injuries, including a torn right ACL that led to reconstructive knee surgery. He tore the same ACL in college at Baylor.

Two plays after Griffin was hurt, Cousins hit fullback Darrel Young for a 20-yard touchdown pass for the game’s first score.

On the Redskins’ next series, Jackson landed on his shoulder after getting tangled with safety Josh Evans on an incomplete pass.

The three-time Pro Bowl receiver was the Redskins’ prized free agency acquisition this year, signing a three-year, $24 million contract with $16 million guaranteed after getting cut by the Eagles.

Nevertheless, the Redskins soon had a 21-0 lead after a pair of 1-yard touchdown runs by Alfred Morris. Morris finished with 85 yards on 22 carries. Niles Paul, playing for sidelined tight end Jordan Reed (hamstring), had a touchdown catch and set career highs with eight catches for 99 yards.

Henne finished 14 of 28 for 193 yards.

Lewis, who scored Jacksonville’s only touchdown, suffered a high ankle sprain on the first play of the third quarter and was carted to the locker room. He did not return.