Wigan took control of the match early on, with Powell coming close to an opening goal when Jasmin Handanovic pushed a chipped effort past the post.
It was Powell who opened the scoring in the 22nd minute when Handanovic failed to deal with a Jean Beausejour cross, allowing the youngster on loan from Manchester United to head home.
Maribor were struggling to create clear opportunities as Wigan's midfield ensured that the hosts dominated possession.
The Latics doubled their lead 11 minutes before the interval when Ben Watson lost his marker inside the box to convert Beausejour's inviting cross.
Powell should have extended his side's advantage even further when he sprinted clear of the Maribor defence but he clipped his shot over the crossbar.
Wigan once again looked dangerous early in the second half and Powell was gifted another chance by Beausejour, whose cross was struck against the post from close range.
Tavares came close again a few minutes later but Scott Carson responded well to keep out the forward's powerful strike.
Maribor looked slightly more dangerous following the goal but they were still being forced onto the back foot by Wigan, who secured the victory when Powell added his second in stoppage time with a drilled finish from the edge of the box.