The Falcons quarterback connected with Drake London on a seven-yard reception with 34 seconds left in the clock.
Kicker Younghoe Koo converted the extra-point attempt, bringing Atlanta right to the edge of their first win of the season.
Safety Jessie Bates III then cinched the victory for the Georgia squad by intercepting Eagles quarterback Jalen Hurts’ last-gasp heave.
The exciting finish was the opposite of a dour opening quarter, with the scoreboard not ticking over until Koo converted a 39-yard field goal attempt at the start of the second quarter.
The Eagles were the first team to find the end zone when DeVonta Smith scored off a seven-yard pass from Hurts, but another Atlanta field goal made it a 7-6 score at half-time.
The floodgates opened from there, both sides trading field goals and touchdowns until a Jake Elliott field goal put Philadelphia up by six with just under two minutes remaining.
The Eagles’ defence were unable to prevent Cousins’ flawless final drive however, the veteran quarterback finishing with two touchdowns and 241 passing yards.