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They were forced to wait until the final three minutes of the second quarter to extend that advantage, as Bernard Pierce burst his way over the line from just a yard out.
Justin Tucker added a 38-yard field goal as time expired in the first half, and added another from the same distance early in the third quarter to take his side into a 20-point lead.
The Ravens edged further ahead in the final minutes, however, as Terrell Suggs got to Ryan in the Falcons' own endzone to sack him for a safety.
They then sealed the victory once and for all with less than two minutes remaining as Flacco combined with Torrey Smith for a 39-yard touchdown to extend their lead to 22 points.
That was how it stayed as the Ravens moved to 5-2 for the season, while the Falcons are left with a 2-5 record.