Gabriel Barbosa's brace helped deliver a stunning 5-0 second-leg win at the Maracana, sealing a comprehensive 6-1 aggregate victory.
The Brazilian side are now through to face defending champions River Plate in their first Libertadores final since 1981.
For head coach Jesus, it is a chance to gain a degree of compensation for the successive Europa League final defeats he suffered while in charge of Benfica.
"Reaching the final is important, but most important is winning the final," said Jesus, who took over at Flamengo in June.
"It's my third continental final. I've unfortunately lost two, one in the 93rd minute against Chelsea [in 2013] and another on penalties against Sevilla [in 2014].
"Only those who get there win. Teams that don't get there will never lose. In Portugal, we often say that we're going to the final to win, and that is what we think."
Bruno Henrique, Pablo Mari and Rodrigo Caio joined star forward Gabigol on the scoresheet in Rio de Janeiro as Flamengo made of mockery of what looked to be a finely poised tie following the 1-1 first-leg draw.
"I'm not thrilled, I'm hoarse," Jesus joked. "Of course, I didn't imagine 5-0. I have a lot of respect for Gremio. I didn't expect it to be easy."
However, he added: "In Porto Alegre, the VAR saved Gremio. I knew today we were going to win the tie. After four months, the team is playing with its eyes closed.
"It's a team that has a lot of confidence. But we have something more important: the pleasure of playing, and that makes my players feel no pressure."