Powell opened the scoring on 22 minutes after capitalising on an error by Maribor goalkeeper Jasmin Handanovic.
Jean Beausejour's deflected cross did not look likely to cause any danger but Handanovic inexplicably punched the ball behind him for Powell to nod into an empty net.
Watson doubled the lead 11 minutes later by powering a header home after excellent work down the left by Beausejour.
Owen Coyle's side had other opportunities to put the game beyond the visitors in the first half with on-loan Manchester United forward Powell at the heart of all Wigan's most promising attacks.
Callum McManaman started to find more space down the right as the half drew to a close and his delicate cross to the back post just evaded Beausejour.
Roberto Martinez, the man who led the Latics to their unlikely FA Cup triumph last season, watched on from the directors' box as his former side made another piece of history.
The hosts should have been out of sight before Maribor captain Tavares pulled a goal back on the hour mark.
Jean-Philippe Mendy forced his way into the area and Tavares was on hand to score past Scott Carson.
Powell then had two further chances to finish the game off but hit the post with one from two yards and then couldn't quite convert a cross minutes later.
Powell did have the final word though, skipping past two Maribor defenders in stoppage time before hammering low past Handanovic.
The result left Wigan well positioned on four points in Group D, two behind Rubin Kazan, who hammered Zulte 4-0 earlier on Thursday and who the Latics play home and away next.