Albion's most recent victory against Sheffield Wednesday came in 2010 thanks to a special long-range strike from the Baggies' former Slovenian midfielder Robert Koren.
The teams have only met twice in competitive matches since Albion's promotion-winning 2009/10 campaign, sharing the spoils in both fixtures last term - drawing 2-2 at Hillsborough and 1-1 at The Hawthorns.
Koren's strike with less than 15 minutes to play fired the Baggies back into second place in the Championship - the position the Throstles would end the season in, to gain promotion.
The 30-yard effort was the highlight of an otherwise quiet battle, although Ishmael Miller, James Morrison and Jonas Olsson were denied second-half goals by Wednesday stopper Lee Grant.