Jones reeled off an 84-yard TD grab in his standout performance, helping stake the Falcons (1-1) to a 24-3 halftime lead.
Matt Ryan went 33-of-43 through the air for 374 yards and a pair of touchdowns as Atlanta rebounded from an opening-week loss to New Orleans.
Osi Umenyiora helped the Falcons' cause with a 68-yard interception return for a score.
The Rams (1-1) rallied with three TD passes from Sam Bradford in the second half, but it wasn't enough to overcome the big deficit.
Rookie Tavon Austin caught two scoring passes for St. Louis.