The German striker opened the scoring after 37 minutes when Kaiserslautern's Rodnei handled the ball inside his own penalty area, allowing Gomez to send goalkeeper Kevin Trapp the wrong way from the spot.
Rodnei was again at fault 10 minutes after halftime when he committed a foul inside the area that sent Gomez to the penalty spot for the second time.
Trapp came up with a save on this attempt, but the rebound was left for a simple finish for Gomez from a few yards.
The hat trick was completed 20 minutes from time when Thomas Muller pulled the ball back to Gomez, allowing him to fire past Trapp and make it 3-0 to Bayern, which has now won its last three games following a loss to open the season.
Bayer Leverkusen 0, Borussia Dortmund 0
Leverkusen, Germany - The top two teams from the Bundesliga last season played to a 0-0 draw at the BayArena on Saturday as Bayer Leverkusen and Borussia Dortmund failed to join the leaders at the top of the table.
A win for either side would have put them level on nine points with Bayern Munich and Werder Bremen, but each team had a player sent off in the second half as Michal Kadlec saw red in the 64th minute for Leverkusen, while Dortmund failed to capitalize as Mario Gotze was sent off 13 minutes later.
Cologne 4, Hamburg 3
Hamburg, Germany - Cologne earned its first win of the season on Saturday as goals from Christian Clemens and Kevin McKenna in the final six minutes gave the visitors a 4-3 win over Hamburg at the Imtech Arena.
Mladen Petric converted a penalty kick in the 11th minute for Hamburg, but his goal was canceled out 10 minutes later by Adil Chihi, making it 1-1 at the break.
Milivoje Novakovic put Cologne ahead early in the second half, but Slobodan Rajkovic and Heung-Min Son scored three minutes apart for Hamburg to put the hosts in front, 3-2.
Clemens tallied the equalizer in the 84th for Cologne and McKenna secured the win a few minutes from time when he pounced on a rebound to fire home the winning goal.
Hamburg has now earned only one point from its first four games.
Freiburg 3, Wolfsburg 0
Freiburg, Germany - Wolfsburg suffered its third successive defeat on Saturday, dropping a 3-0 decision to Freiburg.
First-half goals from Oliver Barth and Erik Jendrisek put Freiburg on its way, while Cedric Makiadi capped the scoring just before the hour mark to wrap up the win.
Freiburg also entered the match having lost two straight games, but the club put in a strong performance to grab its first win of the season.
Werder Bremen 2, Hoffenheim 1
Sinsheim, Germany - Werder Bremen secured its third win in four games to open the new Bundesliga campaign on Saturday, defeating Hoffenheim, 2-1, at the Rhein-Neckar Arena.
Roberto Firmino handed Hoffenheim the lead in the 37th minute, but it was quickly nullified by a goal from Marko Arnautovic one minute later.
The deciding goal arrived seven minutes from time when Claudio Pizarro's cross found Markus Rosenberg, who saw his shot deflect into the net off defender Isaac Vorsah.
Nurnberg 1, Augsburg 0
Nurnberg, Germany - Nurnberg snapped a two-game losing skid on Saturday with a 1-0 win over Augsburg courtesy of a goal from Alexander Esswein 15 minutes from time.
Augsburg was searching for its first win of the season after two draws and a loss to open the campaign, but the difference in the match came in the 75th minute when Tomas Pekhart set up a left-footed shot for Esswein, which found its way inside the far post.