Frear had set up a host of chances before showing his team-mates the way to goal in the 82nd minute when he knocked home from 12 yards after visiting goalkeeper Robby McCrorie had palmed out Chris Cadden’s cross.
Motherwell had already sealed top spot in Group F thanks to a late win over Edinburgh City in midweek and they again toiled against Ladbrokes League Two opposition ahead of their Premiership opener against Rangers.
The Well Society, Motherwell’s majority shareholding fans’ group, invited about 40 Lanarkshire-based Syrian refugees to Fir Park, no doubt expecting to entertain them with a few goals.
But Motherwell’s plans were affected by an early injury to Steven Hammell, which saw Frear come on and Carl McHugh drop into defence.
Louis Moult was making his first start of the season following groin surgery and looked slightly short of match sharpness, although McCrorie made a decent save from the striker after a long ball.
Frear was proving Motherwell’s main threat with his deliveries from the left but a string of headers failed to trouble the goalkeeper, many of them from Moult.
McCrorie, who is on loan from Rangers, made an excellent stop from Moult just after the interval after the striker linked up with Tanner, who then saw a header saved.
Berwick were not just sitting back and Aaron Murrell twice forced saves from Trevor Carson.
Motherwell brought on Alex Fisher and debutant George Newell up front but they too lacked composure in the box.
The hosts forced a string of corners and Charles Dunne had a header cleared off the line before McCrorie helped McHugh’s header on to the bar.
But the breakthrough came from Frear before McCrorie made another good stop from Newell.