Florian Wirtz's penalty gave Xabi Alonso's side a ninth successive win to stretch their lead over Bayern Munich to 16 points with six games remaining.
Bayern gave their title rivals a helping hand by letting a 2-0 lead slip to lose 3-2 at mid-table Heidenheim.
Leverkusen can end their long wait to be crowned German champions by winning at home to Werder Bremen next weekend.
Their coronation, however, is almost inevitable, with Alonso's unbeaten outfit needing just three points from the final 18 available to secure the championship.
Leverkusen will no doubt be keen to finish the job at the first time of asking in front of their own supporters.
They were frustrated in Berlin by several saves from Union keeper Frederik Ronnow, before the breakthrough came in first-half stoppage time after Robin Gosens saw a second yellow card for scything down Nathan Tella.
From the free-kick that followed, Christopher Trimmel handled Piero Hincapie's shot and, following a long video assistant referee check, Wirtz stroked home from the spot.
Leverkusen remain on course for a remarkable treble, having reached the German Cup final in midweek by thrashing Fortuna Dusseldorf 4-0 and they now prepare for the visit of West Ham in the Europa League quarter-final first leg on Thursday.
Line-ups Union Berlin Formation 3-5-2
5Doekhi2Vogt4Monteiro Pinto Leite
28Trimmel29Tousart13Schafer8Khedira6Gosens
7Aaronson14Vertessen
1Ronnow 5Doekhi 2Vogt 4Monteiro Pinto Leite 28TrimmelSubstituted forJuranovicat 63'minutes 29TousartBooked at 37mins 13SchaferSubstituted forKralat 63'minutes 8KhediraSubstituted forLaidouniat 62'minutes 6GosensBooked at 45mins 7AaronsonSubstituted forHollerbachat 79'minutes 14VertessenSubstituted forKaufmannat 45'minutes Substitutes 3Jaeckel 9Kaufmann 11Bedia 16Hollerbach 18Juranovic 20Laidouni 31Knoche 33Kral 37Schwolow B Leverkusen Formation 3-4-2-1
6Kossounou4Tah3Hincapie
19Tella8Andrich34Xhaka20Grimaldo
10Wirtz23Hlozek
1Hradecky 6Kossounou 4Tah 3Hincapie 19TellaSubstituted forFrimpongat 79'minutes 8AndrichBooked at 82mins 34Xhaka 20Grimaldo 10Wirtz 23HlozekSubstituted forAdliat 33'minutesBooked at 64mins 9IglesiasSubstituted forBonifaceat 67'minutes Substitutes 2Stanisic 7Hofmann 12Tapsoba 14Schick 17Kovar 21Adli 22Boniface 25Palacios 30Frimpong Referee: Benjamin Brand Attendance: 22,012 Match Stats Live Text Post update