Dutch striker Klaas-Jan Huntelaar also grabbed two goals, one a penalty, to lead Schalke 04 to a 3-1 win over Hoffenheim that took them up to second.
Forward Vedad Ibisevic levelled for Hoffenheim midway through the second half after Raul had given the hosts a 28th-minute lead with a controversial goal that led the referee to ask the Spaniard if he had used his hand.
"The early goal helped a lot," coach Jupp Heynckes told reporters, referring to Gomez's second-minute opener.
"The team is playing excellent football, is confident with the ball and you can see they are enjoying the game. That is a crucial aspect of being successful."
Claudio Pizarro's 150th Bundesliga goal cancelled out Niko Bungert's 23rd-minute opener for Mainz before Aaron Hunt and Sebastian Proedl sealed the points for Werder.
Heynckes brought back six players, including Gomez, who were rested for Bayern's 6-0 German Cup win over Ingolstadt in the week and his team made a dream start when the Germany forward headed them in front.
On Friday, Michael Ballack's goal gave Bayer Leverkusen a 1-0 win over Freiburg but the former Germany captain also suffered a suspected broken nose that makes him doubtful for the Champions League game with Valencia in the week.
