Plymouth began well enough with a 5-1 from Jack Holder and Stefan Nielsen in the opening race, but Glasgow turned things around to take a two-point lead after four heats.
The visitors extended that advantage to 12 points after 13 heats, clinching victory with two heats to spare.
Overall it was a disappointing evening for the Devils, who produced only five of the 15 race winners.
Their top scorer was Holder with nine (paid 10) from his five rides while Glasgow had Richie Worrall (15 paid 17) and skipper Aaron Summers (12) in double figures.
Plymouth team manager Lee Trigger admitted: “We were found out by a better side and that home defeat means our play-off hopes are severely dented. We had a good crowd, which was a plus for us, and it was a nice summer evening but it hurts to lose at home.”
The result means Plymouth are seven points adrift of sixth-placed Ipswich, who currently occupy the final play-off position, and the Devils now have only four home and two away matches remaining.
Plymouth: Jack Holder 9+1 (5 rides), Stefan Nielsen 6+2 (4), Steve Boxall 3 (4), Todd Kurtz 6 (4), Kyle Newman 8 (5). Reserves: Sam Simota 7+2 (5), Ellis Perks 0 (3).
Glasgow: Aaron Summers 12 (5), rider replacement for Rene Bach, Richie Worrall 15+2 (6), Fernando Garcia 4+1 (4), Richard Lawson 9 (4). Reserves: Nike Lunna 8+2 (7), Tom Bacon 3+1 (4).