Bayern Munich secured a domestic double after beating RB Leipzig 3-0 in the DFB Pokal final at the Olympiastadion in Berlin on Saturday.
Lewandowski sealed Bayern's 19th German Cup soon after, outrunning his defender to a through ball and chipping Gulacsi to make it 3-0 with his 40th goal in all competitions this season.
"It was the toughest opponent we could have had and we saw that in the opening 30 minutes," said Bayern boss Niko Kovac, whose future at the club looks more secure after winning two titles in the past week.
"Manuel Neuer kept us in the game with two superb saves but overall the victory was deserved. We had tough times back in October and November so compliments to the team. To be here with two titles makes me very proud."
Kovac brought on departing club legends Franck Ribery and Arjen Robben for a final runout in front of the Bayern faithful and the two almost combined for a fourth goal in the final match of their illustrious careers in Munich.
The win sees Kovac, who won the double with Bayern as a player too, become the first head coach since Felix Magath in 2005 and 2006 to win back-to-back German Cups after his Frankfurt team beat Bayern in last year's final.
"I am very satisfied with the way we played well and won clearly," Lewandowski said. "We had the game under control and the second half we pushed a bit more and won the Cup.
"We gave everything for the double. At the end we can say that this season was very good for us."