Brescia had led after teenager Sandro Tonali scored his first Serie A goal with a superb long range free-kick after 34 minutes in Genoa.
But after being pegged back for over an hour Motta's side came back with goals from all three second-half substitutes, a first in Serie A history.
Colombian Kevin Agudelo came off the bench after the break and pulled the westerners level after 66 minutes on his Serie A debut.
Christian Kouame acrobatically added a second on 75 minutes and Goran Pandev, who previously played alongside Motta at Inter Milan, adding the third four minutes later to give Genoa their first win in nearly two months.
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"It's a good feeling," said Motta, who replaced Aurelio Andreazzoli, who had garnered just one point from the previous six games.
"The lads were extraordinary from the first to the last minute.
"I asked them to remain united as a team even in difficult moments which they did."
The 37-year-old former PSG, Barcelona and Atletico Madrid player added: "It's nice to see this team write its place in history, but I want to praise everyone, even those who stayed on the bench.
"We showed enormous heart and stayed united throughout every bump in the road, so that is what I am happiest with.
"These are three important goals for Genoa."
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Pandev, 36, was Motta's teammate at Inter Milan as was Brescia's Mario Balotelli, who he won the historic treble with back in 2010.
"I enjoyed meeting Balotelli before the game, we shared historic moments together for Inter," he said.
"We just had a quick chat before kick-off.
"Goran? He calls me Mister."
Former Italy international Motta played for a season with Genoa a decade ago, but his only previous coaching experience was with PSG's U19 team, which he managed until July.
Genoa move out of the relegation zone after their second win of the season and first since September 1.
Balotelli's Brescia slip into the relegation zone with their fifth defeat of the season.
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