Florian Wirtz, who has yet to extend his Leverkusen contract, set up a hat-trick for Schick with a brilliant display and also scored his seventh league goal of the season in Saturday's clash.
The champions dominated but still needed patience before Schick broke the deadlock with a chip over the goalkeeper right before the break.
Wirtz, who'd played Schick through, scored after the break when he displayed brilliant close control to elude a defender before firing the ball inside the near post from a narrow angle.
Vincenzo Grifo pulled one back four minutes later, but Wirtz floated in a precise cross for Schick to head Leverkusen's third in the 67th, then laid the ball back for the Czech to fire Leverkusen's fourth in the 74th.
Schick scored again with a header to a corner three minutes later — the only goal that didn't involve Wirtz.
Leverkusen stayed four points behind Bayern after their eighth straight win across all competitions.
Leverkusen resume their defence at Borussia Dortmund on January 10, while Bayern visit Borussia Monchengladbach the following day.
Brazilian goalkeeper Kaua Santos endured a game to forget as his Eintracht Frankfurt side were shocked 3-1 by 10-man Mainz.
Frankfurt had 34 shots at goal compared to nine by the visitors, who played with a man less from the 21st minute after captain Nadiem Amiri was sent off for catching Ellyes Skhiri's right ankle with his studs.
Santos had already conceded an unfortunate own goal. The keeper played out a short pass to Skhiri, who was immediately under pressure from two Mainz players.
Skhiri sent the ball looping back toward Santos, who deflected it onto the crossbar, from where it rebounded back off the keeper's arm and in.
Mainz's Paul Nebel then scored with a deflected shot for 2-0, and Santos was at fault again when a botched pass invited another Mainz attack. Nebel grabbed his second goal in the 58th.
Rasmus Kristensen, who struck the crossbar in the first half, scored Frankfurt's consolation in the 75th.
Johannes Eggestein fired promoted St Pauli to a 1-0 win at Stuttgart, last season's runner-ups, ending the home side's four-game win streak in all competitions.
It was a huge win for St Pauli's Australian captain Jackson Irvine, who played through injury to inspire the Hamburg-based side.
Union Berlin's winless run stretched to nine games across all competitions as Bo Svensson's team slumped to a 4-1 defeat at Werder Bremen.
Holstein Kiel ended their five-game losing run by routing Augsburg 5-1, while Borussia Monchengladbach won 2-1 at Hoffenheim.
There were tributes with silences observed before all the games for the victims of an attack on a Christmas market in Magdeburg the night before.
"There are always more important things than football," Freiburg coach Christian Günter said.
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