Nathan Tella opened the scoring for Leverkusen after 25 seconds against a makeshift Dortmund defence and Schick made it 2-0 in the eighth and 3-1 in the 19th, in a furious start after Jamie Gittens pulled one back for Dortmund in the 12th.
Serhou Guirassy's 79th-minute penalty revived their hopes again but Leverkusen held on.
Schick now has 11 goals for the season, all in the last seven games including four in the last 2024 match, a 5-1 demolition of Freiburg.
"I was ready and I am happy to have helped the team," Schick said. "It did't matter who played for Dortmund, we had a clear game plan."
Xabi Alonso's Leverkusen recorded their ninth straight victory in all competitions and moved within one point of Bayern, who start 2025 on Saturday with a difficult trip to Borussia Mönchengladbach where they have only won once in their last six outings.
"We are not looking at Bayern but only at ourselves," Leverkusen playmaker Granit Xhaka told streaming portal DAZN.
"If we do well we are on a good path. There are easier opponents than Dortmund for a first game. We are happy for the three points."
Dortmund, who have been plagued by injuries all season, remain sixth and 11 points off the top after their first home defeat of the league season.
"We are used to it and hope that the lads return soon. We have to accept it. Leverkusen have quality but it hurts to have two lads ill at home. We had planned much more," Dortmund captain Julian Brandt said.
A minute of silence was observed before kick-off for ex-Dortmund goalkeeper Wolfgang "Teddy" de Beer who died on December 30 at age 60.
