"It was very weird playing without fans again. We're disappointed because these are the games we know we need to win," assistant coach Achim Beierlorzer, who was standing in for Marsch for the second game in a row, told DAZN.
Moussa Diaby found the net early on for Leverkusen, only for the goal to be ruled out for an offside in the build-up.
They took a deserved lead on 21 minutes, however, Florian Wirtz linking up with Exequiel Palacios to score his fifth goal of the season.
Diaby doubled the lead in style shortly afterwards, plucking a long ball out of the air and drilling a low shot into the bottom corner.
Andre Silva brought Leipzig back into the game with a sharp header on the hour mark, but Leverkusen restored their two-goal lead through Jeremie Frimpong just a few minutes later.
Dominik Szoboszlai crowned a miserable afternoon for the hosts when he slammed a late penalty against the post.
While Leverkusen move up to third, Leipzig's fifth defeat of the season leaves them stuck in mid-table, four points adrift of the Champions League spots.
They are now level on points with 12th-placed Eintracht Frankfurt, who snatched a 2-1 win at home to Union Berlin in Sunday's earlier game.
French defender Evan N'Dicka scored an injury-time header to give Frankfurt their first home win of the season.
After a disappointing start under new coach Oliver Glasner, Frankfurt have now gone six games unbeaten in all competitions.
They have also made a habit of deciding games late on, having scored in injury time in five of their last six games.
"We never give up: that's one of our defining features at the moment," Glasner told DAZN.
"We should have been two or three goals up at half time, but we kept fighting even after the equaliser," he added.
Victory lifted Frankfurt five points clear of the relegation zone, while Union missed another chance to break into the top four after conceding a late goal for the third time in a row away from home.
Frankfurt had an early goal ruled out for offside, but Djibril Sow put them in front with a brilliant half-volley on 22 minutes.
The home side had several chances to double the lead before half-time as they continued to pile pressure on an unsettled Union backline.
Makoto Hasebe hit the bar with a header, while Filip Kostic, Rafael Borre and Kristijan Jakic all missed from close range.
They were made to rue the missed chances when Union equalised on the hour mark.
After a clear foul on Taiwo Awoniyi in the Frankfurt box, Max Kruse slotted in his second league goal of the season from the penalty spot.
Union seemed to have done enough to snatch a point, before N'Dicka rose in the box late in injury time to head home Kostic's cross and seal the three points for Frankfurt.