Germany international Gomez, who came on as a substitute in the 77th minute struck three times in six minutes to complete another big-scoring win this season.
The Bavarians, who won the Bundesliga title earlier this month and face Barcelona in their Champions League semi-final first leg next week, will face either VfB Stuttgart or Freiburg, who play on Wednesday.
"Wolfsburg made it hard for us for a long time," Heynckes told reporters. "We were not fully there at the start. I told them at halftime what I think must change and it seems to have worked.
"I am happy for Mario that he got his hat-trick. It goes to show that we have three top strikers in this team."
Shaqiri, however, restored Bayern's two-goal cushion with an unstoppable low drive from the edge of the box five minutes after the restart and cut back for substitute Gomez to tap in after a darting 20-metre sprint in the 80th minute.
