The victory means Leverkusen have collected 31 of a possible 33 points after 11 matches, equal to the record set by Pep Guardiola's Bayern Munich in 2015-16.
Bayern's 4-2 victory over Heidenheim saw the Bavarians spend Saturday night atop the standings but Alonso's men were dominant on Sunday, winning with goals from Alex Grimaldo, Odilon Kossounou, Jonathan Tah and Nathan Tella.
Leverkusen defender Florian Wirtz cut holes in the Union defence early but striker Victor Boniface was off target, blasting wide twice in the opening minutes.
The home side hit the lead after 24 minutes, Grimaldo stopping on the edge of the box before chipping a dipping shot over Union goalie Frederik Ronnow.
Grimaldo, 28, who was called up to the Spain squad for the first time this week, has six goals in the league since moving from Benfica in the summer.
Union lost centre-back Leonardo Bonucci to injury early and struggled to contain the home side's quick passing, a wide-open Boniface heading directly at Ronnow late in the first half.
Kossounou headed in a Jonas Hofmann corner midway through the second-half to double the home side's lead. It was the Ivorian's goal for Leverkusen in his third season at the club.
Germany centre-back Tah hammered in a corner with just over 15 minutes remaining.
Tella scored two minutes after coming on, the English winger finishing a length-of-the-field attack for his side's fourth.
Leverkusen have now won 16 and drawn one of 17 games in all competitions this season.
Union Berlin, who finished fourth to qualify for the Champions League last season, finish the weekend second from bottom, having lost their last nine in a row.
Later on Sunday, Eintracht Frankfurt take on Werder Bremen while RB Leipzig host Freiburg.
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