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The Giallorossi moved up to third in the fledgling Serie A standings thanks to victory at the Stadio Luigi Ferraris, on a day when they were without Edin Dzeko.
But in the absence of the No. 9 it was Mkhitaryan who certainly stepped up to the plate - scoring the first Giallorossi hat-trick in just over four years to deliver the win.
His first came on the stroke of half-time, the Armenian putting Paulo Fonseca's side ahead with a well-timed header from Jordan Veretout's corner.
Genoa then equalised - through Marko Pjaca - early in the second half, as the game threatened to turn into something of a slog for the visitors.
Instead, Mkhitaryan redoubled his efforts: first running on to Bruno Peres's cutback into the box to steer his side back in front, before clinching the result in the closing stages with a pinpoint volley from Pedro's brilliantly measured cross.
With the international break now to come, Roma head into a two-week break with three wins in the last eight days.
GENOA 1-3 ROMA
SCORERS: Pjaca (50'); Mkhitaryan (47', 66', 85')
GENOA (4-3-2-1): Perin; Biraschi, Masiello (Ghiglione), Bani, Criscito; Lerager (Badelj), Radovanovic (Lu. Pellegrini), Rovella; Zajc (Destro), Pjaca (Pandev); Scamacca
Unused subs: Marchetti, Paleari, Goldaniga, Behrami, Melegoni, Parigini, Czyborra
ROMA (3-4-2-1): Pau Lopez; Mancini, Smalling, Ibanez; Karsdorp, Veretout, Lo. Pellegrini (Villar), Spinazzola (Peres); Pedro, Mkhitaryan; Borja Mayoral (Cristante)
Unused subs: Farelli, Mirante, Jesus, Fazio, Kumbulla, Darboe, Providence, Podgoreanu
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