The Bavarians were leading Wolfsburg 2-1 at the break but the striker's three late goals - after Mario Mandzukic, Arjen Robben and Xherdan Shaqiri had scored - sealed the cup win
It took Mario Mandzukic 17 minutes to fire the hosts into the lead at the Allianz Arena, with Arjen Robben doubling the scoreline 18 minutes later, although Diego Ribas' piledriver on the stroke of half-time made for a potentially nervy second half.
However, Heynckes saw his side sprint out of the blocks with a strike from Xherdan Shaqiri not long after a play resumed and a late hat-trick - three goals in six minutes - from Gomez was the icing on the cake for the dominant Bavarians.
"Wolfsburg made it hard for us for a long time, very hard, especially in the first phase, because in the second half we definitely played better and took advantage of their mistakes," he told reporters after the match.
"You have seen that we have three top strikers [Gomez, Mandzukic and Claudio Pizarro]. I'm happy for Mario that he has managed this hat-trick.
"You can say we have achieved our goal but we did make it hard at times for ourselves. I made it clear during the break what I wanted and what we must change. I think that this was well received."
The German giants, who have already sealed the Bundesliga title, will face either Stuttgart or Freiburg in the DFB-Pokal final.
Die Roten also remain in the hunt for European glory and face Barcelona in the last four of the Champions League, with the first leg on Tuesday April 23.