The 24-year-old rookie notched five hits in a weekend series against the White Sox, and then smacked a game-winning three-run homer against the Padres in Tuesday night's 3-1 victory.
Vargas' sixth-inning shot came on a curveball from San Diego's Jesse Hahn that drifted a bit outside.
"You throw a ball inside or outside, and it doesn't matter," Gardenhire said. "When he gets his arms through right, the ball just takes off like you can't believe."
Vargas skipped Triple-A ball as a result of his callup last week. Gardenhire said while the missed experience at that level means Vargas will have a tougher time getting acclimated to breaking balls at the Major League level, the rookie could have enough power to make up for it.
"He's really strong," Gardenhire said. "[His swing] is not a big long thing. It's pretty quick to the ball. He's just so doggone strong."
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, and follow him on Twitter @RhettBollinger. Alex Smith is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.