The first two were runs, including one for 10 yards and a first down. The third was a pass from quarterback Josh Allen that Moss fumbled and, after passing through a few hands, was recovered by Miami.
For a player who was inactive in Week 1 -- partly due to missing time during training camp dealing with injuries -- and who was benched for most of a game against the 49ers last season due to turnovers, that could have been the end of his day.
But Moss told left tackle Dion Dawkins after the turnover he would take advantage of his next opportunity.
"'Look, the next time I touch this ball, I'm gonna make it count,'" Dawkins recalled Moss telling him. "And he did that two more times."
Coach Sean McDermott went back to the second-year player, who finished with eight carries for 26 yards, two receptions for eight yards, one lost fumble and two rushing touchdowns.
"It was important that he was able to reset and remain mentally tough, come back and he made some really tough runs," McDermott said. " ... That's a great message to everyone and anyone on our football team that you're going to make some mistakes and you've got to be able to come back, get your game back, and that's what your teammates need from you."
Moss had other hurdles to clear off the field this week.
A day before the Week 2 matchup, he spent additional time in South Florida to attend to the funeral of his aunt.
"I had a long weekend. I just lost my -- I had to bury my aunt yesterday morning," Moss said after the game. "Then just having to come out here 24 hours later and have a fumble in a big game that we definitely needed, I had to just kind of get my mental right and kind of just switch over."
But he came back in a significant way, including on his second touchdown after taking a huge hit.
"The level of respect you have for these guys, I think is important. It takes a toll," offensive coordinator Brian Daboll said of the work that players put in. "Then when you go out and you watch them have some success, that ultimately contributes to team success, that's really what you're happy for."
The Bills are working to better incorporate the running game in an offense that has put significant pressure on Allen to perform. Two games into 2021, the quarterback hasn't played at the same level as he did last season -- completing 56% of passes and averaging a career-low 5.3 yards per attempt.
Strengthening the run game, which finished 20th in yards per game last season (107.7), makes the offense more dynamic no matter how Allen is performing, as shown by running back Devin Singletary's 46-yard score to start the game vs. the Dolphins. The team ended the win with 30 run plays (including two kneel downs) to 33 passing attempts.
The coaching staff introduced some new wrinkles for the rushing attack Saturday, and it was effective. While having the lead helped, the Bills’ 143 rushing yards in Miami would have been the fourth-most by the team in a game last year.
The group will continue to adapt to the defense it faces, but there are encouraging signs of progress from last year -- if the offensive line continues to develop, with Singletary leading the way averaging 6.4 yards per attempt and Moss being effective in short-yardage situations.
"We know as running backs that if you don't make (the carries) count down (in the red zone), the chance of you getting another one is very slim," Moss said. "There's a chance that it might go in the air. I just wanted to make sure that when I did get it, I made sure that I had crossed that white line so that we couldn't go in the air and I didn't have to block anyone."