Green-Ellis waited three years for the Patriots to consistently hand him the ball. The yards rarely came in bunches when he finally got his chance, but Green-Ellis arrived at Gillette Stadium yesterday 72 yards shy of 1,000 for the season. With their lead swelling and the Dolphins struggling to keep pace, the Patriots turned their attention to getting Green-Ellis his milestone.

On fourth and 16 from the Miami 19, the Patriots called one more play for Green-Ellis with 14:33 left in the fourth quarter. He sprinted to the right and broke through for a 10-yard gain, landing his first 1,000-yard season. As he trotted off the field, he was flooded with congratulations from his teammates and a hug from coach Bill Belichick.

“It’s not really an individual accomplishment,’’ Green-Ellis said. “If one person said he got 1,000 yards by himself, he’d be lying to you. Everyone worked hard. Everyone comes to practice and works hard in practice Wednesday, Thursday, and Friday, and you know, it’s paying off for us.’’

Green-Ellis rushed for 80 yards on 20 carries and added a touchdown in the Patriots’ 38-7 victory. He became the first Patriot to reach 1,000 yards since Corey Dillon in 2004. He also joined Baltimore’s Ray Rice as the only players this season to rush for more than 1,000 yards without a fumble. His 13 rushing touchdowns this season are the most for the Patriots since 1996.

“That’s really a great accomplishment,’’ quarterback Tom Brady said. “I think the durability of that running back position and to rush the way that our offense has been rushing lately, it’s been great.

“I think there’s really been a strong commitment over the course of the season to make yards in the run game and keep things balanced and use our run to set up play-action. It’s definitely been a huge threat. Benny should be pretty proud. It’s pretty cool for him.’’

During the game, running back Fred Taylor, who has rushed for more than 1,000 yards seven times in his career, reminded Green-Ellis to keep all of the mementos, from gloves to shoes, as reminders of the achievement. As soon as Green-Ellis reached 1,000 yards, Taylor charged down the sideline for the ball.

“I tried to make sure I ran and got it for him,’’ Taylor said. “I think Coach Belichick was headed in that same direction, but Benny stopped and hugged him. He can’t leave any of that stuff out. It’s a special moment.’’

In 2008, Green-Ellis was an undrafted free agent out of the University of Mississippi. The Patriots signed him and eventually added him to the practice squad before the season opener. A few months later he was promoted to the active roster, but he was used sparingly. Last season, Green-Ellis was inactive for four games in the regular season and had 26 carries for 114 yards.

It wasn’t long before Green-Ellis worked his way into the regular rotation this season. The Patriots traded Laurence Maroney and placed Kevin Faulk on injured reserve. Taylor was hampered by turf toe, so the running game fell on the shoulders of Green-Ellis and Danny Woodhead.

Throughout the season, Green-Ellis said he leaned on his fellow running backs, including Sammy Morris. There were moments when Green-Ellis would watch film with Taylor or seek advice from Faulk. In return, his teammates were rooting for him.

“Going into this game that was one of the things we definitely tried to get done, along with the win, first and foremost,’’ Taylor said. “As he got closer, everybody was just wanting to stay in there and wanting him to get it. He deserves it — 14-2 is amazing and 14-2 with a 1,000-yard rusher [along with] Tom’s play speaks for itself. That’s all the better.

“[Tight end Rob] Gronkowski doing what he’s doing as a rookie, it’s a good time. These are memories. [Running backs coach Ivan Fears] was talking [Saturday night] that you want to create these memories. For Benny, he’ll never forget it.’’

For the Patriots, Green-Ellis has been a player who could best be described by the results he’s produced on the field, Belichick said.

“I think that’s one of the biggest things about Benny is his consistency — training camp, regular season, preseason, and all the way through,’’ Belichick said. “I think he’s been really consistent.’’

Monique Walker can be reached at mwalker@globe.com.