The Poland striker showed clinical finishing to tuck away an Alphonso Davies second-half pass at the Allianz Arena to claim his 13th league goal and set a new record for scoring in the first nine Bundesliga games of the season.
Lewandoski, on the mark in each of his last 13 games for Bayern, overtook the previous league record set by current Arsenal forward Pierre-Emerick Aubameyang who scored in each of the first eight games of the 2015/16 season for Borussia Dortmund.
Lewandowski also scored twice in Bayern’s 3-2 midweek win at Olympiakos in the Champions League, leaving the 31-year-old with 19 goals in just 14 appearances in all competitions during what is turning into the best season of his career.
Lewandowski is already the top-scoring foreigner in Bundesliga history with 215 league goals for Bayern and former club Dortmund.
Bayern quickly took charge at the Allianz Arena as defender Benjamin Pavard gave the hosts the lead before Lewandowski’s second just after the break.
At the other end, Bayern captain Manuel Neuer saved a Sebastian Anderson penalty on 59 minutes and not to be outdone, Union’s Poland goalkeeper Ralf Gikiewicz denied Bayern winger Serge Gnabry from close range.
Lewandowski looked to have claimed a second, but his effort six minutes from time was ruled out.
Union grabbed a late consolation goal when replacement striker Sebastian Polter netted from the penalty spot having been brought down by Pavard.
Munich can lose top spot Sunday to previous leaders Moenchengladbach, who host Eintracht Frankfurt, and Wolfsburg who can leap-frog Niko Kovac’s Bayern by beating Augsburg at home.
Dortmund moved up to third after a goalless draw at Schalke, who had the better chances in the Ruhr derby.
Schalke centre-back Salif Sane headed onto the crossbar with nearly half an hour played and soon after midfielder Suat Serdar hit the post.
Schalke’s Welsh striker Rabbi Matondo, 19, wasted three clear chances, while at the other end Dortmund playmaker Marco Reus and England winger Jadon Sancho went close for the visitors.
Freiburg went second after bouncing back from last weekend’s shock defeat at Union to earn a 2-1 win at home to RB Leipzig.
After beating Zenit Saint-Petersburg in the Champions League in mid-week, Leipzig came unstuck as Nicolas Hoefler gave Freiburg the lead on the stroke of half-time before striker Nils Petersen came off the bench to add a second on 90 minutes.
Lukas Klostermann scored a consolation goal for Leipzig.
Bottom side Paderborn earned their first win this season as defender Sebastian Schonlau and midfielder Abdelhamid Sabiri scored in a 2-0 win at home to Fortuna Duesseldorf.
Mid-table Hoffenheim earned their third straight success, having beaten Bayern and Schalke, with Benjamin Huebner scoring late in their 3-2 win at Hertha Berlin.