Foreman led the way for the Panthers in wet conditions in Charlotte, North Carolina, rushing for 130 yards and a touchdown from 31 carries.
Neither side has set the NFL alight this season, and the game began in sluggish fashion as both offences struggled to build any momentum in the rain.
After striking first blood with a field goal, Carolina extended their lead to 10 in the second quarter when Laviska Shenault Jr outran the Atlanta defence on a 41-yard touchdown run.
The Falcons were eventually able to get on the scoreboard thanks to a 33-yard field goal from Younghoe Koo just before half time.
The visitors cut the deficit to four midway through the third quarter when quarterback Marcus Mariota connected with Drake London on a seven-yard touchdown pass.
However, the Panthers hit back through Foreman to push the lead back out to 10 headed into the fourth quarter.
An early field goal from Carolina kicker Eddy Pineiro looked to have all but sealed the result, until Mariota found KhaDarel Hodge in the end zone with two minutes left to keep their hopes alive.
But it was ultimately not meant to be, as Pineiro converted a 40-yard attempt as the clock wound down to clinch the Panthers' third win of the season.