Having won the first leg 3-2 at home, Sampdoria had to hold their nerve at the Lombardian club before Pozzi struck in the 91st minute.
With 10,000 fans watching the game back in Genoa on a big screen in the city's Piazzale Kennedy, Samp won promotion after spending a single season in the second division.
The Blucerchiati join Torino and Pescara as the three promoted teams from Serie B, replacing relegated Lecce, Novara and Cesena.
Coach Giuseppe Iachini dedicated Sampdoria's achievement to "our extraordinary fans".
"I always believed we could do it even when things were difficult," he said. "Will I stay at the club? Yeah, I hope so."
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