Leverkusen had flown out of the blocks, taking the lead inside two minutes through Jeremie Frimpong in the capital before Jeong Woo-yeong struck back for the hosts to restore parity before the break.
But the champions found a winner in the 71st minute, with Czech forward Schick meeting Florian Wirtz's cross to settle a finely balanced game in their favour.
Leverkusen are now six points behind Bayern, who play Borussia Dortmund in the Klassiker later on Saturday.
Wolfsburg pulled off a shock 5-1 win at RB Leipzig, giving former Leipzig coach Ralph Hasenhuettl a triumphant return to his former club.
Leipzig endured a nightmare start, with Wolfsburg leading 2-0 inside the first five minutes.
Algerian striker Mohamed Amoura opened the scoring in the fourth minute, with Tiago Tomas doubling the advantage a minute later.
Amoura added his second after 16 minutes, and Joakim Maehle piled on the misery for the hosts after the break.
Leipzig captain Willi Orban tapped in a late consolation, but it was too little, too late, as Leipzig conceded four for the second consecutive league game.
Hasenhuettl, who coached Leipzig during their first two seasons in the German top flight, completed a perfect afternoon when his two substitutes combined for a fifth, with Mattias Svanberg laying it on a plate for Kevin Behrens.
Leipzig are now winless in six games, including four in the league, after their fast start to the season, slipping to fourth. In contrast, Wolfsburg have climbed to seventh and are unbeaten in their last five league games.
Elsewhere, Freiburg held off Borussia Moenchengladbach to win 3-1 and bounce back from their 4-0 trouncing in Dortmund last weekend.
Freiburg led 2-0 through Lucas Hoeler and Ritsu Doan.
Gladbach halved the deficit through Germany striker Tim Kleindienst, but no sooner had they found a way back than Hoeler struck again to make it three.
Stuttgart striker Ermedin Demirovic scored a brace as the visitors twice fought back to secure a 2-2 draw at Werder Bremen.
In the day's other match, a first-half penalty by Phillip Tietz gave Augsburg a 1-0 win over Bochum, who remain rooted to the bottom of the table with two points.
