Alabama kicker Andy Pappanastos missed a 36-yard field goal that would have won it for the Crimson Tide at the end of regulation.
In overtime, Rodrigo Blankenship kicked a 51-yard field goal on Georgia’s first possession after Jake Fromm was sacked on third down to give the Bulldogs a 23-20 lead.
Devin Bellamy sacked Tagovailoa on the Crimson Tide's first play of the overtime to put Alabama in second-and-26.
On the next play, Alabama stunned Georgia when Tagovailoa found Smith running wide open down the left sideline.
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Alabama denied Georgia its first national championship since 1980.
The win gives Crimson Tide head coach Nick Saban his sixth national title, matching the record set by former Alabama coach Paul "Bear" Bryant.
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Tagovailoa finished 14-for-24 with 166 yards passing and three touchdowns.
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Georgia quarterback Jake Fromm went 16-for-32 with 232 yards with one touchdown and two interceptions.