On-loan Manchester United forward Powell profited from a goalkeeping howler to become the first Wigan player to score in the Europa League in Thursday night's Group D clash at home to Maribor.
FA Cup hero Ben Watson made it two before half-time at the DW Stadium. Tavares took advantage of profligacy from Powell to pull one back and would have levelled matters in the 90th minute but for a stunning save from Scott Carson.
However, a fine individual goal from Powell wrapped up a 3-1 win which put the Latics second in their pool.
The 19-year-old is more comfortable in midfield but injuries to Grant Holt and Marc-Antoine Fortune meant he was pushed into a striking role, and he could easily have had five or six goals.
Powell joined United in 2012 from boyhood club Crewe and scored on his Premier League debut against Wigan last September.
His loan spell with Coyle's team runs until the end of the season, and the manager believes the 19-year-old has the potential to follow in the footsteps of two other young players he has helped move forward in their careers.
Jack Wilshere and Daniel Sturridge both played for Coyle on loan at Bolton and are set for key roles in England's forthcoming World Cup qualifiers.
Coyle said of Powell: "That's why we brought him here because I believe he's a top player in the making and nights like this will certainly help.
"He's got so much to offer. I want it on a consistent basis, and I'm trying to demand that of him to help him progress his career.
"I've been fortunate to be able to do that before with a couple of very good players and I see Nick Powell in that category.
"I've no doubt when you see Jack Wilshere and Daniel Sturridge, the level they're playing at, both England players, I truly believe that in time Nick Powell can attain that level.
"To do that he's got to bring performances like this on a consistent basis and show that after his year's loan, when he goes back to Manchester United, that he's in a position to challenge for their first team.
"And if he is, given the level they play at, that would then push him towards the England limelight. He's a bit off that yet but he's certainly got the ingredients that we can help to move him forward."