Pogba bossed midfield on the artificial pitch and fired United ahead in the 35th minute with a goal of the highest quality, drilling a left-foot shot into the top corner from the edge of the penalty area after side-stepping his marker.
The France World Cup winner made it 2-0 with a contentious 44th-minute penalty, harshly awarded by German referee Deniz Aytekin after Luke Shaw's cross struck Kevin Mbabu's arm as the defender tried to avoid contact.
A darting run by Pogba midway through the second half released Anthony Martial and the forward scored with a clinical finish from eight metres after his compatriot's good work left him with time and space to find the back of the net.
Roared on by a vocal home crowd, Young Boys charged at United in the opening 30 minutes, forcing two saves by David De Gea as the Spain goalkeeper kept out long-range efforts from Mohamed Ali Camara and Christian Fassnacht.
United's defence looked vulnerable on either flank to the home team's breakaways, although 19-year-old Portuguese right back Diogo Dalot showed pace going forward on his debut for the Premier League side.
After Marcus Rashford clipped the outside of the post with a flicked shot in the 22nd minute, United's nerves were settled when Pogba broke the deadlock out of nothing thanks to a piece of sublime individual skill.
Young Boys' hopes of a comeback evaporated after Pogba confidently converted the penalty and Martial, enjoying a rare start up front, made no mistake at the near post as United maintained cruise control in the second half.
(Writing by Zoran Milosavljevic; Editing by Ed Osmond)
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