Shipperley headed home his fourth goal of the season after 10 minutes, with keeper Romain Larrieu allowing a point blank effort to bobble in.
But the Blades sealed the win on the half-hour when Quinn drilled a 20-yard free-kick through a crowded area.
Plymouth manager Tony Pulis
"We created enough to be pleased with the performance, but I'm disappointed with the goals we conceded.
"We were caught in possession a few times in dangerous areas and there is a
lot of work to be done.
"But I saw some encouraging signs. They might have had most of the possession but we created the better chances. It was important not to crumble at 2-0."
Sheff Utd: Kenny, Bromby, Morgan, Kozluk, Unsworth, Jagielka, Ifill (Gillespie 69), Quinn, Montgomery, Shipperley (Pericard 64), Kabba (Webber 78).
Subs Not Used: Tonge, Geary.
Booked: Montgomery, Shipperley, Kozluk.
Goals: Shipperley 10, Quinn 31.
Plymouth: Larrieu, Barness, Brevett (Djordjic 56), Doumbe, Aljofree, Norris, Chadwick (Taylor 57), Capaldi, Wotton, Gudjonsson (Buzsaky 57), Evans.
Subs Not Used: West, McCormick.
Booked: Wotton, Barness.
Ref: D Laws (Tyne & Wear).