By
Josip Ilicic had pulled the visitors level just before the break after Andrea Bertolacci had put Genoa ahead after only four minutes.
But Masiello's header seven minutes into the second half clinched the points in a game which had been pushed back a day because of snow in northern Italy.
The victory margin would have been even wider for the visitors but for some crucial saves by home goalkeeper Mattia Perin.
"We fought until the end," said Masiello.
"This year everything is more difficult, it's hard in the league with our Europa League commitments."
Atalanta -- through to the last 32 in Europe where they meet German side Borussia Dortmund -- move up to eighth in Serie A, with Genoa just two points above the relegation zone.