The 24-year-old scored twice in the first half of Sturrock's first game back at the West Country club, little more than 24 hours after his appointment as manager in succession to Ian Holloway.
A late strike from substitute Jermaine Easter could not deny West Bromwich Albion a deserved win.
Bednar was making his first start for West Brom after a loan move from Hearts and was included only because of an injury to Ishmael Miller.
It took him just nine minutes to open his account, latching on to Zoltan Gera's right-wing cross to get behind the Argyle back four and slide the ball past a static Argyle goalkeeper Romain Larrieu.
Gera was also the architect of what turned out to be the winning goal, releasing left-winger Chris Brunt with a 60-yard diagonal pass from the right wing to the left.
Brunt, who played under Sturrock at Sheffield Wednesday, had plenty of time and space to cross for Bednar to stoop and head the ball home.
West Brom continued to turn on the style, playing with pace and flair that makes them look a sure bet to return to the Premiership, and only Argyle's determination kept them in the game.
The second half was more of an even affair, although Bednar went close to completing his hat-trick when Larrieu made a hash of Gera's long pass forward. However, the Argyle keeper recovered to keep out his chip.
The home side was rewarded for their grit with a goal six minutes from time from substitute Easter.
The Wales international striker latched on to a pass from David Norris to fire home a first goal since his loan move from Wycombe Wanderers, giving Baggies' goalkeeper Dean Kiely no chance.
It proved too little, too late for Argyle and West Brom went home with three deserved points.