Talisca was the difference for the Primeira Liga side as he fired home the only goal of the game with eight minutes remaining in Lisbon, his first goal in the competition.
Benfica had dominated large parts of the Group C clash, but were wasteful in front of goal until the 20-year-old's late strike from a Derley flick.
Jesus hailed the resilience of his side and set his sights firmly on their clash with Zenit later this month as three teams battle it out for a top-two place.
"We now have a light at the end of the tunnel," said Jesus. "If we did not win the dream was over, but now we can start to think of the match against Zenit, which will be extremely important.
"Leverkusen have practically qualified, so now the fight will be between us, Monaco and Zenit.
"We had to win. Only the victory counted.
"We made a good game and we deserved this victory, as we had the best chances.
"Monaco always defend well, they are very strong defensively and they showed it once again. We knew that it was fundamental to score first and we did."
Benfica's victory moves them level with Zenit on four points in the table, one behind second-placed Monaco, while Bayer Leverkusen are top with nine.
