Their 7-0 lead was doubled to 14-0 when Darrell Henderson rushed one in from eight yards out, and after a Falcons field goal, the Rams added their third touchdown of the half with a three-yard fade to the back corner of the endzone for Cooper Kupp.
Reigning Offensive Player of the Year Kupp nabbed his second of the game after half-time, getting on the end of a 10-yard pass to make it 28-3. He went on to finish with 11 catches from 14 targets for 108 yards and two touchdowns, after snagging 13 catches for 128 yards and a touchdown in Week 1.
While the game appeared dead, nobody told the Falcons as they began to march back into the contest.
The first receiver taken in this year's NFL Draft – Drake London, at pick eight – gave the Falcons their first touchdown of the night, and the first of his career, when he reeled in a four-yard pass from Marcus Mariota.
Another field goal for the Rams would extend their lead to 31-10, which was cut to 31-17 when Olamide Zaccheaus found some space for an 11-yard touchdown reception with eight minutes remaining.
The Rams clearly felt they had done enough for the win, and were content to punt the ball away on their next drive, only for the punt to get blocked, scooped up and run in by Lorenzo Carter for a Falcons touchdown, with a two-point conversion cutting the deficit to 31-25.
Atlanta would get a chance to drive down and win the game after Kupp coughed up an uncharacteristic fumble, but Mariota's pass into the endzone was picked off by Jalen Ramsey, allowing the Rams to run out the clock, even taking an intentional safety in the process to drain the time.
Stafford completed 27 of 36 passes for 272 yards, three touchdowns and two interceptions, and with Falcons running back Damien Williams placed on injured reserve, Cordarrelle Patterson and Tyler Allegier split the carries with 10 each.
Wilson's Broncos ride to choppy first win
The Broncos trailed 6-3 in the final seconds of the first half, and with fourth-and-goal at the one yard line they opted to trot out the kicker, which was met with a chorus of boos for the coaching decision.
After an interception on the opening drive of the second half, Wilson himself was met with boos as he had only completed six-of-18 passes up until that point, but a touchdown pass to Eric Saubert at the start of the fourth quarter was enough to get the Broncos over the line.
Wilson ended up completing 14 of his 31 passes for 219 yards, one touchdown and one interception, and he relied heavily on receiver Courtland Sutton, who reeled in seven of his 11 targets for 122 yards.