The Red Devils were comfortable right from the start as Nani had the first shot in the 16th minute from outside the box but it curled off target.
Just moments later United surged ahead. Shinji Kagawa picked up the ball from deep and passed it to Ryan Giggs, who then released Wayne Rooney on the left for the striker to send in a cross for Antonio Valencia to slot in from close range.
United doubled their advantage on the half-hour mark when Emir Spahic inadvertently turned Rooney's free kick inside his own net.
Bayer stepped up their game after the interval as Stefan Reinartz headed against the visitors' post in the 60th minute.
However, David Moyes's side virtually wrapped up the points and with it qualification to the last 16 of the competition five minutes later when Evans poked the ball into the home team's goal from just two yards out after Bernd Leno had kept out Rooney's initial effort on goal.
Chris Smalling made it 4-0 13 minutes from time with an easy finish after latching on to Rooney's pass and Nani completed the rout in the 88th minute with a clipped effort over Leno from a tight angle.