Claudio Pizarro had spells at Bayern Munich, Chelsea and Cologne before returning to Werder Bremen in 2018.
Peru bounced back from their agonizing opening defeat vs Brazil to beat 10-man Venezuela 1-0.
Pep Guardiola's Bayern remain second in the table, but are now level with Dortmund on both goal difference and points after their win in Gelsenkirchen.
Pizarro, who scored four goals in Bayern's 9-2 German league rout of Hamburg in March, has made more than 350 Bundesliga appearances, scoring 166 goals, both of which are records for foreigners in Germany's top-flight.
A 6-1 victory at Hanover on Saturday gave Bayern a Bundesliga-record 26th victory this season, a record ninth consecutive away win, while they also equalled Dortmund's previous best of 81 points in a single season.
Bayern paid Stuttgart 30 million euros for Gomez in 2009 and his market value is around 35 million euros ($US45.89m) having scored 71 goals in 109 Bundesliga appearances for Munich.
One point from their remaining seven matches and the Bavarians - who have managed 10 wins on a roll - will be crowned champions, ending two years of Dortmund domination.
Argentina rode their luck to come away from Lima with a 1-1 draw against Peru and maintain their slender one-point lead at the top of the World Cup 2014 South American qualifying table.
Despite scoring 41 goals in 52 games for Bayern Munich last season, Mario Gomez is unsure of his place in the team.
Peru striker Claudio Pizarro is returning to Bayern Munich on a free transfer after a five-year absence.