The Trojans took an early lead when Marley Grant latched onto Archie White’s through before rounding Jody Barford to score.
The Zebras responded with Luke Sellers, Owen Vincent and Stephen McCarron coming close.
McCarron then had an effort cleared off the goal line as Brigg continued to search for an equalizer.
Afterwards, Vincent was denied by goalkeeper Addison Bliss before McCarron’s shot flew just wide on the stroke of half time.
In the second half, substitute Joe Pugh fired inches wide soon after replacing Conner Harman.
Minutes later Martin Pembleton raced clear and forced Bliss into a good save.
Staveley doubled their lead against the run of play through Max Rhodes, who drove a 20-yarder into the bottom left corner.
Late on the Trojans almost added a third goal with Clark Greaves rattling the crossbar.
The Zebras were disappointed to lose 2-0 despite creating the most chances. Better finishing is required in next week’s trip to Horbury Town.