The Packers took the lead on the final play of the opening quarter when Eddie Lacy burst over the line from just a yard out.
Ryan then threw his second touchdown pass of the match when he picked out a free Tony Gonzalez in the endzone from just two yards.
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Mason Crosby kicked a 40-yard field goal to reduce the deficit to four, but the Falcons extended it further before half time when Sean Weatherspoon intercepted Matt Flynn's pass before returning it 71 yards for a touchdown.
The Packers responded in the third quarter, closing the gap with two field goals from Crosby to make it 21-16 going into the fourth.
They began the final quarter well, taking the lead when Flynn threw a two-yard pass to Andrew Quarless, who collected well under pressure in the endzone.
The Packers went for a two-point conversion but Flynn's pass to James Jones was incomplete, making it a one-point game going into the closing stages.
Neither side could add to their tally in the remaining minutes, however, as the Packers held on for a valuable victory at a snowy Lambeau Field.